Nested Hilbert schemes on surfaces: virtual fundamental class

DOI10.1016/j.aim.2020.107046zbMath1437.14054arXiv1701.08899OpenAlexW3006100509MaRDI QIDQ2308302

Artan Sheshmani, Amin Gholampour, Shing Tung Yau

Publication date: 2 April 2020

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.08899

zbMATH Keywords

projective surfacesvirtual fundamental classnested Hilbert scheme

Mathematics Subject Classification ID

Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Parametrization (Chow and Hilbert schemes) (14C05)

Related Items

Defects, nested instantons and comet-shaped quivers, Equivariant \(K\)-theory and refined Vafa-Witten invariants, Notes on fundamental algebraic supergeometry. Hilbert and Picard superschemes, Virasoro constraints for moduli of sheaves and vertex algebras, Vafa-Witten invariants for projective surfaces I: stable case, Degeneracy loci, virtual cycles and nested Hilbert schemes II, Monopole contributions to refined Vafa-Witten invariants, Verlinde formulae on complex surfaces: K-theoretic invariants, Vertical Vafa-Witten invariants, Virtual χ−y‐genera of Quot schemes on surfaces, Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics

Cites Work

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• A proof of the Göttsche-Yau-Zaslow formula
• Exts and vertex operators
• Algebraic cobordism of bundles on varieties
• Universal polynomials for tautological integrals on Hilbert schemes
• On the homology of the Hilbert scheme of points in the plane
• A short proof of the Göttsche conjecture
• Good degeneration of Quot-schemes and coherent systems
• Deformation-obstruction theory for complexes via Atiyah and Kodaira-Spencer classes
• Poincaré invariants
• Algebraic cobordism revisited
• The Betti numbers of the Hilbert scheme of points on a smooth projective surface
• Localization of virtual classes
• Chern classes of tautological sheaves on Hilbert schemes of points on surfaces
• The intrinsic normal cone
• Cellular decompositions for nested Hilbert schemes of points
• A degeneration formula of GW-invariants
• Stable morphisms to singular schemes and relative stable morphisms.
• Intersection numbers on the relative Hilbert schemes of points on surfaces
• Donaldson-Thomas invariants of 2-dimensional sheaves inside threefolds and modular forms
• Projectivity of complete moduli
• Poincaré invariants are Seiberg-Witten invariants
• Degeneracy loci, virtual cycles and nested Hilbert schemes. I
• Shuffle algebras associated to surfaces
• Complexe cotangent et déformations. I. (The cotangent complex and deformations. I.)
• Universal polynomials for singular curves on surfaces
• A theory of generalized Donaldson–Thomas invariants
• Curves on K 3 surfaces and modular forms
• Reduced classes and curve counting on surfaces I: theory
• Stable pairs and BPS invariants
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• Degeneracy loci, virtual cycles and nested Hilbert schemes II
• Localizing virtual cycles by cosections
• Gromov–Witten theory and Donaldson–Thomas theory, I
• Gromov–Witten theory and Donaldson–Thomas theory, II
• Truncated Hilbert functors.