相关论文: Wall-Crossings in Toric Gromov-Witten Theory II: L…

Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…

We conjecture the existence of almost integer invariants governing the all-genus equivariant Gromov-Witten theory of Calabi-Yau fivefolds with a torus action. We prove the conjecture for skeletal, locally anti-diagonal torus actions by…

Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving multiple covers of genus 0 curves to the…

We study here the crepant resolution correspondence for the torus equivariant descendent Gromov-Witten theories of Hilb(C2) and Sym(C2).The descendent correspondence is obtained from our previous matching of the associated CohFTs by…

We investigate Gromov-Witten invariants associated to exceptional classes for primitive birational contractions on a Calabi-Yau threefold X. It was observed in a previous paper that these invariants are locally defined, in that they can be…

We study stable maps to normal crossings pairs with possibly negative tangency orders. There are two independent models: punctured Gromov-Witten theory of pairs and orbifold Gromov-Witten theory of root stacks with extremal ages. Exploiting…

The Remodeling Conjecture proposed by Bouchard-Klemm-Marino-Pasquetti [arXiv:0709.1453, arXiv:0807.0597] relates all genus open and closed Gromov-Witten invariants of a semi-projective toric Calabi-Yau 3-manifolds/3-orbifolds to the…

For an arbitrary integer $r\geq 1$, we compute $r$-framed motivic PT and DT invariants of small crepant resolutions of toric Calabi-Yau $3$-folds, establishing a "higher rank" version of the motivic DT/PT wall-crossing formula. This…

We prove the cohomological crepant resolution conjecture of Ruan for the weighted projective space P(1,3,4,4). To compute the quantum corrected cohomology ring we combine the results of Coates-Corti-Iritani-Tseng on P(1,1,1,3) and our…

We prove the crepant transformation conjecture for relative Grassmann flops over a smooth base $B$. We show that the $I$-functions of the respective GIT quotients are related by analytic continuation and a symplectic transformation. We…

We use the mirror theorem for toric Deligne-Mumford stacks, proved recently by the authors and by Cheong-Ciocan-Fontanine-Kim, to compute genus-zero Gromov-Witten invariants of a number of toric orbifolds and gerbes. We prove a mirror…

A bicyclic pair is a smooth surface equipped with a pair of smooth divisors intersecting in two reduced points. Resolutions of self-nodal curves constitute an important special case. We investigate the logarithmic Gromov-Witten theory of…

In this note, we describe a a systematic procedure to find toric crepant resolutions of orbifold vertex, and show that the generating series of certain disc invariants of the orbifold vertex can be suitably identified with the generating…

In this paper, we study the all genus Gromov-Witten theory for any GKM orbifold $X$. We generalize the Givental formula which is studied in the smooth case in \cite{Giv2} \cite{Giv3} \cite{Giv4} to the orbifold case. Specifically, we…

In this paper, we give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying new relations in the tautological ring of the moduli space of 2-pointed…

We introduce a global Landau-Ginzburg model which is mirror to several toric Deligne-Mumford stacks and describe the change of the Gromov-Witten theories under discrepant transformations. We prove a formal decomposition of the quantum…

We use the Gromov-Witten/Pairs descendent correspondence for toric 3-folds and degeneration arguments to establish the GW/P correspondence for several compact Calabi-Yau 3-folds (including all CY complete intersections in products of…

We state a version of the crepant resolution conjecture for total ancestor potentials for surface singularities, and reduce the conjecture to the quantum McKay correspondence conjecture of J.Bryan and A.Gholampour and a vanishing conjecture…

The BKMP Remodeling Conjecture \cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion \cite{EO07} on its mirror curve. The proof of the…