Localization of virtual classes

DOI10.1007/s002220050293zbMath0953.14035arXivalg-geom/9708001OpenAlexW2034404907MaRDI QIDQ1283488

Rahul Pandharipande, Tom Graber

Publication date: 13 June 1999

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9708001

zbMATH Keywords

moduli spacesequivariant cohomologylocalizationGromov-Witten invariantmoduli stacksenumerative geometryDeligne-Mumford stacktautological ringvirtual fundamental classpointed curvesequivariant Chow groupexcess integral

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35)

Related Items

Stable pair invariants under blow-ups, Lie groupoids, deformation of unstable curves, and construction of equivariant Kuranishi charts, A virtual fundamental class construction for the moduli space of \((\mathbb{C}^\ast)^n\)-equivariant morphisms, Real Gromov-Witten theory in all genera and real enumerative geometry: construction, Orbifold Gromov-Witten theory of weighted blowups, On orbifold Gromov-Witten theory in codimension one, Hodge integrals and invariants of the unknot, On the kappa ring of \(\overline{\mathcal{M}}_{g, n}\), All loop topological string amplitudes from Chern-Simons theory, Stable quotients and the holomorphic anomaly equation, Wall-crossing between stable and co-stable ADHM data, Ruan cohomologies of the compactifications of resolved orbifold conifolds, Quantum cohomology of the Hilbert scheme of points in the plane, A Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic, Tautological classes on the moduli spaces of stable maps to \(\mathbb {P}^r\) via torus actions, Hurwitz theory and the double ramification cycle, Virtual intersections on the Quot scheme and Vafa-Intriligator formulas, Open Gromov-Witten invariants of toric Calabi-Yau 3-folds, Instantons, topological strings, and enumerative geometry, Moduli stacks of stable toric quasimaps, A new gluing recursive relation for linear sigma model of \(\mathbb P^1\)-orbifold, Stable quasimaps to GIT quotients, Descendent theory for stable pairs on toric 3-folds, Orbifold quasimap theory, The quantum orbifold cohomology of weighted projective spaces, Quadratic recursion relations of Hodge intervals via localization, Moduli of ADHM sheaves and the local Donaldson-Thomas theory, Quantum Kirwan morphism and Gromov-Witten invariants of quotients. III, Quivers, line defects and framed BPS invariants, A remark on Gromov-Witten invariants of quintic threefold, Orbifold Gromov-Witten theory of the symmetric product of \(\mathcal A_{r}\), Polynomial families of tautological classes on \(\mathcal M^{\mathrm{rt}}_{g,n}\), Hypertoric geometry and Gromov-Witten theory, Strengthening the cohomological crepant resolution conjecture for Hilbert-Chow morphisms, The moduli space of stable quotients, A conjectural formula for genus one Gromov-Witten invariants of some local Calabi-Yau \(n\)-folds, The \(\varkappa \) ring of the moduli of curves of compact type, Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds, Mirror symmetry for stable quotients invariants, Localization computation of one-point disk invariants of projective Calabi-Yau complete intersections, Quantum \(K\)-theory. I: Foundations, Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I, The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture, Ruan's conjecture on singular symplectic flops of mixed type, Gromov-Witten/pairs descendent correspondence for toric 3-folds, Takagi lectures on Donaldson-Thomas theory, Getzler's relation by localization, Gauged linear sigma model for disc invariants, Quantum Kirwan morphism and Gromov-Witten invariants of quotients. II, Weighted Euler characteristic of the moduli space of higher rank Joyce-Song pairs, GW/PT descendent correspondence via vertex operators, A product formula for log Gromov-Witten invariants, Torus localization and wall crossing for cosection localized virtual cycles, Virtual classes for the working mathematician, Brane actions, categorifications of Gromov-Witten theory and quantum \(K\)-theory, Lower bounds for enumerative counts of positive-genus real curves, Rational reductions of the 2D-Toda hierarchy and mirror symmetry, Two point extremal Gromov-Witten invariants of Hilbert schemes of points on surfaces, The quantum tropical vertex, Abelian Hurwitz-Hodge integrals, Integral transforms and quantum correspondences, Hodge-GUE correspondence and the discrete KdV equation, Local Gromov-Witten invariants and tautological sheaves on Hilbert schemes, Lower degree curves in \(X_{3,3} \subset \mathbb{P} ^2 \times \mathbb{P} ^2\), Relative maps and tautological classes, Mukai flop and Ruan cohomology, Group actions on stacks and applications, Knot invariants from topological recursion on augmentation varieties, The local Donaldson-Thomas theory of curves, The equivariant Atiyah class, The virtual \(K\)-theory of Quot schemes of surfaces, The theory of \(N\)-mixed-spin-\(P\) fields, Local Gromov-Witten invariants of canonical line bundles of toric surfaces, The Hodge-FVH correspondence, Connecting Hodge integrals to Gromov-Witten invariants by Virasoro operators, Blow-up formulae of high genus Gromov-Witten invariants for threefolds, Vertical Vafa-Witten invariants, Higher-genus wall-crossing in the gauged linear sigma model, Virtual intersection theories, Gromov-Witten invariants of blow-ups along submanifolds with convex normal bundles, A mathematical theory of the topological vertex, Gromov-Witten theory of \(A_{n}\)-resolutions, Virtual fundamental classes via dg-manifolds, Wall-crossing in genus-zero hybrid theory, The logarithmic gauged linear sigma model, Algebraic cobordism revisited, Computing genus-zero twisted Gromov-Witten invariants, The 3-fold vertex via stable pairs, Polynomial structure of Gromov-Witten potential of quintic \(3\)-folds, Curve counting via stable pairs in the derived category, Riemann-Roch theorems and elliptic genus for virtually smooth schemes, Quasimap wall-crossing for GIT quotients, Virtual equivariant Grothendieck-Riemann-Roch formula, Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics, Local Gromov-Witten invariants of cubic surfaces via nef toric degeneration, Instanton partition functions and M-theory, \(SO\)(3) monopoles, level-one Seiberg--Witten moduli spaces, and Witten's conjecture in low degrees, Virasoro constraints for target curves, Relative virtual localization and vanishing of tautological classes of moduli spaces of curves, Functoriality in intersection theory and a conjecture of Cox, Katz, and Lee, EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS, Extremal Gromov-Witten invariants of the Hilbert scheme of Points, On the global quotient structure of the space of twisted stable maps to a quotient stack, Moduli of $J$-holomorphic curves with Lagrangian boundary conditions and open Gromov-Witten invariants for an $S^1$-equivariant pair, Counting sheaves on Calabi-Yau 4-folds. I, A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds, Boundaries \& localisation with a topological twist, The cohomological Hall algebra of a surface and factorization cohomology, Congruences on K-theoretic Gromov-Witten invariants, Formal groups and quantum cohomology, Gromov–Witten theory of complete intersections via nodal invariants, The 4-fold Pandharipande-Thomas vertex, The virtual intersection theory of isotropic Quot schemes, Logarithmic Gromov-Witten theory and double ramification cycles, A wall-crossing formula for Gromov-Witten invariants under variation of git quotient, Verlinde/Grassmannian correspondence and rank 2 \(\delta\)-wall-crossing, Gromov-Witten invariants of 𝑆𝑦𝑚^{𝑑}ℙ^{𝕣}, Correspondence of Donaldson-Thomas and Gopakumar-Vafa invariants on local Calabi-Yau 4-folds over \(V_5\) and \(V_{22}\), Virasoro Constraints for Toric Bundles, On weighted-blowup formulae of genus zero orbifold Gromov–Witten invariants, Wall-crossing for vortex partition function and handsaw quiver variety, Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds, Stable maps to Looijenga pairs, Marked relative invariants and GW/PT correspondences, Application of Lagrange inversion to wall-crossing for Quot schemes on surfaces, Unnamed Item, Unnamed Item, Magnificent four, Localization and gluing of orbifold amplitudes: The Gromov-Witten orbifold vertex, The Candelas-de la Ossa-Green-Parkes formula, THE KATZ–KLEMM–VAFA CONJECTURE FOR SURFACES, The local Gromov-Witten theory of curves, Hodge integrals and integrable hierarchies, On the crepant resolution conjecture in the local case, A combinatorial case of the abelian-nonabelian correspondence, HIGHER GENUS GROMOV–WITTEN THEORY OF AND ASSOCIATED TO LOCAL CURVES, The Gromov–Witten invariants of the Hilbert schemes of points on surfaces with p_g > 0, Gromov–Witten Theory of $\text{K3} \times {\mathbb{P}}^1$ and Quasi-Jacobi Forms, The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves, Higher genus quasimap wall-crossing for semipositive targets, Equivariant Gromov-Witten invariants of algebraic GKM manifolds, Elliptic Gromov-Witten Invariants of Del-Pezzo Surfaces, On the mathematics and physics of Mixed Spin P-Fields, Counting twisted sheaves and S-duality, Double nested Hilbert schemes and the local stable pairs theory of curves, Polynomiality of the equivariant Gromov-Witten theory of $mathbb P^{r-1}$, Localization and mirror symmetry, A brief introduction to cosection localization and 𝑃-fields, Open \(\mathbb{CP}^1\) descendent theory. I: The stationary sector, Twisted sheaves and \(\text{SU}(r) / {\mathbb{Z}}_r\) Vafa-Witten theory, An effective theory of GW and FJRW invariants of quintics Calabi-Yau manifolds, On the structure of certain natural cones over moduli spaces of genus-one holomorphic maps, Tetrahedron instantons, Unnamed Item, Virtual cycles on projective completions and quantum Lefschetz formula, Quantum Serre duality for quasimaps, A mirror construction for the big equivariant quantum cohomology of toric manifolds, Lagrangian Floer theory on compact toric manifolds. I., Double ramification cycles on the moduli spaces of curves, A survey on mixed spin P-fields, The loop equation for special cubic Hodge integrals, Virtual classes of \(\mathbb{G}_{\mathrm{m}}\)-gerbes, Global mirrors and discrepant transformations for toric Deligne-Mumford stacks, Atiyah class and sheaf counting on local Calabi Yau fourfolds, Three-partition Hodge integrals and the topological vertex, On Gromov-Witten theory of projective bundles, Quasimap wall-crossings and mirror symmetry, Holomorphic anomaly equations for the formal quintic, Virasoro constraints for stable pairs on toric threefolds, Equivariant \(K\)-theory and refined Vafa-Witten invariants, Gromov-Witten/Pairs correspondence for the quintic 3-fold, Virtual signed Euler characteristics, Towards logarithmic GLSM: the \(r\)-spin case, Transversally elliptic complex and cohomological field theory, Chamber structure and wallcrossing in the ADHM theory of curves. I, Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds II: Fano 3-folds, On orbifold Gromov-Witten classes, Vafa-Witten invariants for projective surfaces I: stable case, The quantum McMay correspondence for singularities of type D, Virtual pullbacks in K-theory, Unnamed Item, Localization for logarithmic stable maps, Mixed Frobenius structure and the local A-model, Equivariant GW theory of stacky curves, Spectral theory and mirror symmetry, Descendents for stable pairs on 3-folds, On the Gopakumar–Ooguri–Vafa correspondence for Clifford–Klein 3-manifolds, Graph sums in the remodeling conjecture, Higher genus relative and orbifold Gromov-Witten invariants, Monopole contributions to refined Vafa-Witten invariants, Gromov-Witten invariants under blow-ups along \((-1,-1)\)-curves, Localizing virtual structure sheaves for almost perfect obstruction theories, Quantum $q$-Langlands Correspondence, Localizing virtual fundamental cycles for semi-perfect obstruction theories, Verlinde formulae on complex surfaces: K-theoretic invariants, New topological recursion relations, Descendents on local curves: rationality, Genus-decreasing relation of Gromov-Witten invariants for surfaces under blow-up, An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg–Witten Invariants, A Note on a Generalization of the Multiple Cover Formula and the Simple Flop, Floer theory for negative line bundles via Gromov-Witten invariants, Birational cobordism invariance of uniruled symplectic manifolds, Quantum McKay correspondence for disc invariants of toric Calabi-Yau 3-orbifolds, Virtual manifolds and localization, The enumerative geometry of $K3$ surfaces and modular forms, Quantum cohomology of the Hilbert scheme of points on 𝒜_{𝓃}-resolutions, On explicit formulae of LMOV invariants, A mirror theorem for the mirror quintic, Higher-genus wall-crossing in Landau-Ginzburg theory, Enumerative geometry of Calabi-Yau 4-folds, Higher rank K-theoretic Donaldson-Thomas Theory of points, On the remodeling conjecture for toric Calabi-Yau 3-orbifolds, Virtual χ−y‐genera of Quot schemes on surfaces, Nested Hilbert schemes on surfaces: virtual fundamental class, Moduli spaces of stable quotients and wall-crossing phenomena, Donaldson–Thomas theory of 𝒜_n×P¹, Weighted-blowup correspondence of orbifold Gromov-Witten invariants and applications, A string dual for partially topological Chern-Simons-matter theories, Recursive formula for 𝜓^{𝑔}-𝜆₁𝜓^{𝑔-1}+⋯+(-1)^{𝑔}𝜆_{𝑔} in \overline{ℳ}_{ℊ,1}, Relative Gromov-Witten invariants of projective completions of vector bundles, A short proof of the λg -conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves, Cobordism invariants of the moduli space of stable pairs, Quantum cohomology and toric minimal model programs, Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local, A quantum splitting principle and an application, Motivic virtual signed Euler characteristics and their applications to Vafa-Witten invariants, A formula of two-partition Hodge integrals, Energy bounds and vanishing results for the Gromov-Witten invariants of the projective space, Open Gromov-Witten invariants from the augmentation polynomial, Open/closed correspondence via relative/local correspondence, Localization and gluing of topological amplitudes, Quasimaps to GIT fibre bundles and applications, Unnamed Item, Tangent curves to degenerating hypersurfaces, Enumerative geometry, before and after string theory, Computation of open Gromov-Witten invariants for toric Calabi-Yau 3-folds by topological recursion, a proof of the BKMP conjecture, Narrow quantum \(D\)-modules and quantum Serre duality, A quantum modification of relative Chen-Ruan cohomology, Effective computations of the Atiyah-Bott formula