Generating series of stable pairs descendent invariants on Fano 3-folds are rational and q ↔ q^{-1} symmetric.
Joyce,Enumerative invariants and wall-crossing formulae in abelian categories
5 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.
Cohomological descendent series for Quot schemes on surfaces with pg=0 are rational for nonzero beta and N>1.
Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.
Generalizes Joyce vertex algebras to non-linear enumerative problems and constructs twisted modules in the orthosymplectic case, proposing variants for different enumerative invariants.
citing papers explorer
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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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Rationality of cohomological descendent series for Quot schemes on surfaces with $p_g=0$
Cohomological descendent series for Quot schemes on surfaces with pg=0 are rational for nonzero beta and N>1.
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The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds
Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.
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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.