Curve counting theories via stable objects I. DT/PT correspondence

DOI10.1090/S0894-0347-10-00670-3zbMath1207.14020arXiv0902.4371MaRDI QIDQ3160721

Yukinobu Toda

Publication date: 8 October 2010

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

Full work available at URL: https://arxiv.org/abs/0902.4371

Mathematics Subject Classification ID

Related Items (56)

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 ⋮ Double nested Hilbert schemes and the local stable pairs theory of curves ⋮ Hall algebras and curve-counting invariants ⋮ Introduction to Donaldson–Thomas and Stable Pair Invariants ⋮ A proof of the Donaldson-Thomas crepant resolution conjecture ⋮ Curve counting via stable objects in derived categories of Calabi-Yau 4-folds ⋮ Refined, motivic, and quantum ⋮ Stability on a triangulated category and moduli ⋮ Stability conditions and birational geometry of projective surfaces ⋮ Stability conditions and extremal contractions ⋮ Rank 𝑟 DT theory from rank 1 ⋮ Categorical and K-theoretic Donaldson–Thomas theory of (part II) ⋮ Flops and the S-duality conjecture ⋮ Virasoro constraints for stable pairs on toric threefolds ⋮ Gromov-Witten/Pairs correspondence for the quintic 3-fold ⋮ INTRINSIC STABILIZER REDUCTION AND GENERALIZED DONALDSON–THOMAS INVARIANTS ⋮ The local categorical DT/PT correspondence ⋮ Chamber structure and wallcrossing in the ADHM theory of curves. II ⋮ Stability conditions and curve counting invariants on Calabi-Yau 3-folds ⋮ Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex ⋮ Counting perverse coherent systems on Calabi-Yau 4-folds ⋮ Motivic measures of moduli spaces of 1-dimensional sheaves on rational surfaces ⋮ Curve counting and DT/PT correspondence for Calabi-Yau 4-folds ⋮ Topological string partition function on generalised conifolds ⋮ Moduli of Bridgeland semistable objects on 3-folds and Donaldson-Thomas invariants ⋮ Reduced Donaldson-Thomas invariants and the ring of dual numbers ⋮ Multiple cover formula of generalized DT invariants. I: Parabolic stable pairs ⋮ Descendents for stable pairs on 3-folds ⋮ Quotient categories, stability conditions, and birational geometry ⋮ Takagi lectures on Donaldson-Thomas theory ⋮ Tilt-stability, vanishing theorems and Bogomolov-Gieseker type inequalities ⋮ The DT/PT correspondence for smooth curves ⋮ S-duality for surfaces with \(A_n\)-type singularities ⋮ GW/PT descendent correspondence via vertex operators ⋮ Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities ⋮ Hall-type algebras for categorical Donaldson-Thomas theories on local surfaces ⋮ THE KATZ–KLEMM–VAFA CONJECTURE FOR SURFACES ⋮ Stable pairs, flat connections and Gopakumar-Vafa invariants ⋮ Curve counting theories on Calabi-Yau 3-folds: Approach via stability conditions on derived categories ⋮ Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds ⋮ Affine pavings for moduli spaces of pure sheaves on \(\mathbb P^2\) with degree \(\leq 5\) ⋮ Orientations for DT invariants on quasi-projective Calabi-Yau 4-folds ⋮ The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds ⋮ Sheaves of maximal intersection and multiplicities of stable log maps ⋮ Combinatorics of the double-dimer model ⋮ Combinatorics of the double-dimer model ⋮ The local motivic DT/PT correspondence ⋮ Moduli spaces of stable quotients and wall-crossing phenomena ⋮ Cobordism invariants of the moduli space of stable pairs ⋮ Quasimaps and stable pairs ⋮ \(K\)-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds ⋮ Relative Donaldson-Thomas theory for Calabi-Yau 4-folds ⋮ Orientability for gauge theories on Calabi-Yau manifolds

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