Hall algebras and curve-counting invariants

DOI10.1090/S0894-0347-2011-00701-7zbMath1234.14039arXiv1002.4374MaRDI QIDQ3173300

Tom Bridgeland

Publication date: 27 September 2011

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.4374

zbMATH Keywords

Hall algebramotivic integrationgenerating seriesBehrend functioncurve countingstable pairDT invariantPT invariant

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Stacks and moduli problems (14D23)

Related Items (54)

Hilbert schemes and stable pairs: GIT and derived category wall crossings ⋮ A theory of generalized Donaldson–Thomas invariants ⋮ Stable pair invariants under blow-ups ⋮ A relation between higher-rank PT-stable objects and quotients of coherent sheaves ⋮ Curve counting theories via stable objects I. DT/PT correspondence ⋮ Double nested Hilbert schemes and the local stable pairs theory of curves ⋮ Donaldson-Thomas invariants and flops ⋮ Donaldson-Thomas theory and cluster algebras ⋮ Introduction to Donaldson–Thomas and Stable Pair Invariants ⋮ A proof of the Donaldson-Thomas crepant resolution conjecture ⋮ On reduced stable pair invariants ⋮ Translation quiver varieties ⋮ Descendent theory for stable pairs on toric 3-folds ⋮ Rank 𝑟 DT theory from rank 1 ⋮ Flops and the S-duality conjecture ⋮ Virasoro constraints for stable pairs on toric threefolds ⋮ Gromov-Witten/Pairs correspondence for the quintic 3-fold ⋮ The local categorical DT/PT correspondence ⋮ The Thom-Sebastiani theorem for the Euler characteristic of cyclic \(L_\infty\)-algebras ⋮ Gentle algebras arising from surfaces with orbifold points of order 3. I: Scattering diagrams ⋮ Stability conditions and curve counting invariants on Calabi-Yau 3-folds ⋮ A proof of N. Takahashi's conjecture for \(( \mathbb{P}^2, E)\) and a refined sheaves/Gromov-Witten correspondence ⋮ Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex ⋮ Counting perverse coherent systems on Calabi-Yau 4-folds ⋮ Curve counting and DT/PT correspondence for Calabi-Yau 4-folds ⋮ Topological string partition function on generalised conifolds ⋮ Reduced Donaldson-Thomas invariants and the ring of dual numbers ⋮ Multiple cover formula of generalized DT invariants. I: Parabolic stable pairs ⋮ An introduction to motivic Hall algebras ⋮ Descendents for stable pairs on 3-folds ⋮ DONALDSON–THOMAS INVARIANTS OF LOCAL ELLIPTIC SURFACES VIA THE TOPOLOGICAL VERTEX ⋮ Takagi lectures on Donaldson-Thomas theory ⋮ The DT/PT correspondence for smooth curves ⋮ Riemann-Hilbert problems from Donaldson-Thomas theory ⋮ S-duality for surfaces with \(A_n\)-type singularities ⋮ Descendents on local curves: rationality ⋮ GW/PT descendent correspondence via vertex operators ⋮ Rank 2 wall-crossing and the Serre correspondence ⋮ Hall-type algebras for categorical Donaldson-Thomas theories on local surfaces ⋮ THE KATZ–KLEMM–VAFA CONJECTURE FOR SURFACES ⋮ Donaldson-Thomas invariants versus intersection cohomology of quiver moduli ⋮ Curve counting invariants for crepant resolutions ⋮ On the crepant resolution conjecture for Donaldson-Thomas invariants ⋮ Curve counting theories on Calabi-Yau 3-folds: Approach via stability conditions on derived categories ⋮ Scattering diagrams, sheaves, and curves ⋮ Combinatorics of the double-dimer model ⋮ Combinatorics of the double-dimer model ⋮ The local motivic DT/PT correspondence ⋮ Motivic classes of generalized Kummer schemes via relative power structures ⋮ Cobordism invariants of the moduli space of stable pairs ⋮ \(K\)-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds ⋮ Parabolic refined invariants and Macdonald polynomials ⋮ Some Quot schemes in tilted hearts and moduli spaces of stable pairs ⋮ Donaldson–Thomas invariants of abelian threefolds and Bridgeland stability conditions

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