Generating series of stable pairs descendent invariants on Fano 3-folds are rational and q ↔ q^{-1} symmetric.
2021), arXiv: 2111.04694v1
6 Pith papers cite this work. Polarity classification is still indexing.
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Defines generalized Hodge-Riemann and Bogomolov pairs of cohomology classes, conjectures the former imply the latter, proves cases, and obtains new boundedness theorems for semistable sheaves.
Multiple cover formulas for reduced descendent GW invariants on K3 and abelian surfaces are implied by the conjectural families GW/PT correspondence, with the PT side proven via cosections and universality.
PT generating functions with descendents are rational, with controlled poles, for superpositive curve classes on projective complex 3-folds.
Generalizes Joyce vertex algebras to non-linear enumerative problems and constructs twisted modules in the orthosymplectic case, proposing variants for different enumerative invariants.
Cohomological descendent generating series for Quot schemes of rank-0 quotients of O_S^⊕N on surfaces with p_g=0 are rational when β≠0 and N>1.
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Rationality and symmetry of stable pairs generating series of Fano 3-folds
Generating series of stable pairs descendent invariants on Fano 3-folds are rational and q ↔ q^{-1} symmetric.
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Generalized Bogomolov Inequalities
Defines generalized Hodge-Riemann and Bogomolov pairs of cohomology classes, conjectures the former imply the latter, proves cases, and obtains new boundedness theorems for semistable sheaves.
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The multiple cover formula for $K3$ and abelian surfaces
Multiple cover formulas for reduced descendent GW invariants on K3 and abelian surfaces are implied by the conjectural families GW/PT correspondence, with the PT side proven via cosections and universality.
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The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds
PT generating functions with descendents are rational, with controlled poles, for superpositive curve classes on projective complex 3-folds.
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Modules and generalizations of Joyce vertex algebras
Generalizes Joyce vertex algebras to non-linear enumerative problems and constructs twisted modules in the orthosymplectic case, proposing variants for different enumerative invariants.
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Rationality of cohomological descendent series for Quot schemes on surfaces with $p_g=0$
Cohomological descendent generating series for Quot schemes of rank-0 quotients of O_S^⊕N on surfaces with p_g=0 are rational when β≠0 and N>1.