Related papers: Higher-genus wall-crossing in Landau-Ginzburg theo…

We study genus zero wall-crossing for a family of moduli spaces introduced recently by Fan-Farvis-Ruan. The family has a wall and chamber structure relative to a positive rational parameter. For a Fermat quasi-homogeneous polynomial W (not…

The hybrid model is the Landau-Ginszburg-type theory that is expected, via the Landau-Ginzburg/Calabi-Yau correspondence, to match the Gromov-Witten theory of a complete intersection in weighted projective space. We prove a wall-crossing…

For a Fermat quasi-homogeneous polynomial $W$, we study a family of K-theoretic quantum invariants parametrized by a positive rational number $\epsilon$. We prove a wall-crossing formula by showing the generating functions lie on the…

We give a new proof of Ciocan-Fontanine and Kim's wall-crossing formula relating the virtual classes of the moduli spaces of $\epsilon$-stable quasimaps for different $\epsilon$ in any genus, whenever the target is a complete intersection…

We define a generalization of Fan-Jarvis-Ruan-Witten theory, a "hybrid" model associated to a collection of quasihomogeneous polynomials of the same weights and degree, which is expected to match the Gromov-Witten theory of the Calabi-Yau…

We reconstruct the all-genus Fan-Jarvis-Ruan-Witten invariants of a Fermat cubic Landau-Ginzburg space $(x_1^3+x_2^3+x_3^3: [\mathbb{C}^3/ \mathbold{\mu}_3]\to \mathbb{C})$ from genus-one primary invariants, using tautological relations and…

In previous work (arXiv:1304.7056) we have conjectured wall-crossing formulas for genus zero quasimap invariants of GIT quotients and proved them via localization in many cases. We extend these formulas to higher genus when the target is…

In this paper, we prove a wall-crossing formula for $\epsilon$-stable quasimaps to GIT quotients conjectured by Ciocan-Fontanine and Kim, for all targets in all genera, including the orbifold case. We prove that stability conditions in…

The Landau-Ginzburg/Calabi-Yau correspondence claims that the Gromov-Witten invariant of the quintic Calabi-Yau 3-fold should be related to the Fan-Jarvis-Ruan-Witten invariant of the associated Landau-Ginzburg model via wall crossings. In…

We introduce a technique for proving all-genus wall-crossing formulas in the gauged linear sigma model as the stability parameter varies, without assuming factorization properties of the virtual class. We implement this technique explicitly…

Let $W$ be a quasi-homogeneous polynomial of general type and $<J>$ be the cyclic symmetry group of $W$ generated by the exponential grading element $J$. We study the quantum spectrum and asymptotic behavior in Fan-Jarvis-Ruan-Witten theory…

We prove an explicit formula for the genus-one Fan-Jarvis-Ruan-Witten invariants associated to the quintic threefold, verifying the genus-one mirror conjecture of Huang, Klemm, and Quackenbush. The proof involves two steps. The first step…

Wall-crossing formulas for various flavors of elliptic genus can be obtained using master spaces. We give a topological criterion which implies that such wall-crossing formulas are trivial. Applications are given for: GIT quotients,…

We compute the recently introduced Fan-Jarvis-Ruan-Witten theory of W-curves in genus zero for quintic polynomials in five variables and we show that it matches the Gromov-Witten genus-zero theory of the quintic three-fold via a symplectic…

For each positive rational number epsilon, the theory of epsilon-stable quasimaps to certain GIT quotients W//G developed in arXiv:1106.3724[math.AG] gives rise to a Cohomological Field Theory. Furthermore, there is an asymptotic theory…

For a target variety $X$ and a nodal curve $C$, we introduce a one-parameter stability condition, termed $\epsilon$-admissibility, for maps from nodal curves to $X\times C$. If $X$ is a point, $\epsilon$-admissibility interpolates between…

In this paper, we prove a K-theoretic wall-crossing formula for $\epsilon$-stable quasimaps for all GIT targets in all genera. It recovers the genus-0 K-theoretic toric mirror theorem by Givental-Tonita and the genus-0 mirror theorem for…

We prove the genus-one restriction of the all-genus Landau-Ginzburg/Calabi-Yau conjecture of Chiodo and Ruan, stated in terms of the geometric quantization of an explicit symplectomorphism determined by genus-zero invariants. This provides…

In the last three years a new concept -- the concept of wall crossing has emerged. The current situation with wall crossing phenomena, after papers of Seiberg-Witten, Gaiotto-Moore-Neitzke, Vafa-Cecoti and seminal works by Donaldson-Thomas,…

We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…