50 citations · 406 across the 26 of their papers we have counts for
27 papers
-theoretic pullbacks for Lagrangians on derived critical loci
Yalong Cao, Yukinobu Toda, Gufang Zhao
Given a regular function on a smooth stack, and a -shifted Lagrangian on the derived critical locus of , under fairly general hypotheses, we construct a pullback m…
A degeneration formula of Donaldson-Thomas theory on local Calabi-Yau 4-folds
Yalong Cao, Gufang Zhao, Zijun Zhou
We define relative Donaldson-Thomas invariants of local log Calabi-Yau 4-folds, under the assumption that the derived Hilbert scheme on the anti-canonical divisor is a derived crit…
Quasimaps to quivers with potentials
Yalong Cao, Gufang Zhao
This paper is concerned with a non-compact GIT quotient of a vector space, in the presence of an abelian group action and an equivariant regular function (potential) on the quotien…
A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
Yalong Cao, Martijn Kool, Sergej Monavari
Let be a finite subgroup of whose elements have age not larger than one. In the first part of this paper, we define -theoretic stable pair invariants on the…
Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
Yalong Cao, Georg Oberdieck, Yukinobu Toda
Using reduced Gromov-Witten theory, we define new invariants which capture the enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are analogous to the…
Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
Yalong Cao, Georg Oberdieck, Yukinobu Toda
As an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold using Gromov-Witten theory.…
Gopakumar-Vafa invariants of fiber classes on Calabi-Yau 4-folds fibered over curves
Yalong Cao, Feng Qu
We prove a conjectural correspondence of Cao-Maulik-Toda which relates Gopakumar-Vafa invariants of fiber classes on a smooth projective Calabi-Yau 4-fold fibered over a curve to t…
Counting perverse coherent systems on Calabi-Yau 4-folds
Yalong Cao, Yukinobu Toda
Nagao-Nakajima introduced counting invariants of stable perverse coherent systems on small resolutions of Calabi-Yau 3-folds and determined them on the resolved conifold. Their inv…
Tautological stable pair invariants of Calabi-Yau 4-folds
Yalong Cao, Yukinobu Toda
Let be a Calabi-Yau 4-fold and a smooth divisor on it. We consider tautological complex associated with on the moduli space of Le Potier stable pairs a…
Stable pair invariants of local Calabi-Yau 4-folds
Yalong Cao, Martijn Kool, Sergej Monavari
In 2008, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold using Gromov-Witten theory. Recently, Cao-Maulik-Toda proposed a conjectural descript…
Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions
Yalong Cao, Yukinobu Toda
The Gopakumar-Vafa type invariants on Calabi-Yau 4-folds (which are non-trivial only for genus zero and one) are defined by Klemm-Pandharipande from Gromov-Witten theory, and their…
Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
Yalong Cao, Yukinobu Toda
In our previous paper with Maulik, we proposed a conjectural Gopakumar-Vafa (GV) type formula for the generating series of stable pair invariants on Calabi-Yau (CY) 4-folds. The pu…
Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
Yalong Cao, Martijn Kool
Recently, Cao-Maulik-Toda defined stable pair invariants of a compact Calabi-Yau 4-fold . Their invariants are conjecturally related to the Gopakumar-Vafa type invariants of …
Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
Yalong Cao, Davesh Maulik, Yukinobu Toda
As an analogy to Gopakumar-Vafa conjecture on CY 3-folds, Klemm-Pandharipande defined GV type invariants on CY 4-folds using GW theory and conjectured their integrality. In this pa…
Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
Yalong Cao, Jacob Gross, Dominic Joyce
This paper concerns orientability of moduli spaces of Spin(7)-instantons on compact 8-manifolds with Spin(7)-structure for the Lie groups SU() and U(), and of moduli spac…
Counting zero-dimensional subschemes in higher dimensions
Yalong Cao, Martijn Kool
Consider zero-dimensional Donaldson-Thomas invariants of a toric threefold or toric Calabi-Yau fourfold. In the second case, invariants can be defined using a tautological insertio…
Counting conics on sextic 4-folds
Yalong Cao
We study rational curves of degree two on a smooth sextic 4-fold and their counting invariant defined using Donaldson-Thomas theory of Calabi-Yau 4-folds. By comparing it with the…
Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
Yalong Cao, Davesh Maulik, Yukinobu Toda
In analogy with the Gopakumar-Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi-Yau 4-folds using Gromov-Witten theory and conjectured the…
Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds II: Fano 3-folds
Yalong Cao
In analogy with the Gopakumar-Vafa (GV) conjecture on Calabi-Yau (CY) 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi-Yau 4-folds using Gromov-Witten theory a…
Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
Yalong Cao, Martijn Kool
We study Hilbert schemes of points on a smooth projective Calabi-Yau 4-fold . We define invariants by integrating the Euler class of a tautological vector bundle…
Remarks on Kawamata's effective non-vanishing conjecture for manifolds with trivial first Chern classes
Yalong Cao, Chen Jiang
Kawamata proposed a conjecture predicting that every nef and big line bundle on a smooth projective variety with trivial first Chern class has nontrivial global sections. We verify…
Mukai flops and Plücker type formulas for hyper-Kähler manifolds
Yalong Cao, Naichung Conan Leung
We study the intersection theory of complex Lagrangian subvarieties inside holomorphic symplectic manifolds. In particular, we study their behaviour under Mukai flops and give a ri…
Remarks on mirror symmetry of Donaldson-Thomas theory for Calabi-Yau 4-folds
Yalong Cao, Naichung Conan Leung
Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results fro…
Relative Donaldson-Thomas theory for Calabi-Yau 4-folds
Yalong Cao, Naichung Conan Leung
Given a complex 4-fold with an (Calabi-Yau 3-fold) anti-canonical divisor , we study relative Donaldson-Thomas invariants for this pair, which are elements in the Donaldson-…