## 58 Citations

Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system

- Mathematics
- 2012

We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in…

Global Mirrors and Discrepant Transformations for Toric Deligne-Mumford Stacks

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2020

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…

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

- Mathematics
- 2012

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan,…

Monodromy at infinity of A-hypergeometric functions and toric compactifications

- Mathematics
- 2008

We study non-confluent A-hypergeometric systems introduced by Gelfand et al. (Funct Anal Appl 23:94–106, 1989) and prove a formula for the eigenvalues of their monodromy automorphisms defined by the…

The Hilb/Sym correspondence for C2: descendents and Fourier-Mukai

- Mathematics
- 2018

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…

On the better behaved version of the GKZ hypergeometric system

- Mathematics
- 2010

We consider a version of the generalized hypergeometric system introduced by Gelfand, Kapranov and Zelevinsky (GKZ) suited for the case when the underlying lattice is replaced by a finitely generated…

Logarithmic Frobenius manifolds, hypergeometric systems and quantum D-modules

- Mathematics
- 2010

We describe mirror symmetry for weak toric Fano manifolds as an equivalence of D-modules equipped with certain filtrations. We discuss in particular the logarithmic degeneration behavior at the large…

Quantum Cohomology and Periods

- Mathematics
- 2011

In a previous paper, the author introduced a Z-structure in quantum cohomology defined by the K-theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds.…

## References

SHOWING 1-10 OF 31 REFERENCES

Maximal degeneracy points of GKZ systems

- Mathematics
- 1996

Motivated by mirror symmetry, we study certain integral representations of solutions to the Gel’fand-Kapranov-Zelevinsky(GKZ) hypergeometric system. Some of these solutions arise as period integrals…

The orbifold Chow ring of toric Deligne-Mumford stacks

- Mathematics
- 2004

Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which correspond to combinatorial data. The main result in this paper is an explicit calculation of the orbifold Chow ring of a…

Rational Hypergeometric Functions

- MathematicsCompositio Mathematica
- 2001

Multivariate hypergeometric functions associated with toric varieties were introduced by Gel'fand, Kapranov and Zelevinsky. Singularities of such functions are discriminants, that is, divisors…

Hypergeometric functions and mirror symmetry in toric varieties

- Mathematics
- 1999

We study aspects related to Kontsevich's homological mirror symmetry conjecture in the case of Calabi-Yau complete intersections in toric varieties. In a 1996 lecture at Rutgers University,…

Resonant Hypergeometric Systems and Mirror Symmetry

- Mathematics
- 1997

In Part I the Γ-series of [11] are adapted so that they give solutions for certain resonant systems of Gel’fand-Kapranov-Zelevinsky hypergeometric differential equations. For this some complex…

Homological methods for hypergeometric families

- Mathematics
- 2004

We analyze the behavior of the holonomic rank in families of holonomic systems over complex algebraic varieties by providing homological criteria for rank-jumps in this general setting. Then we…

String Cohomology of a Toroidal Singularity

- Mathematics
- 1998

We construct explicitly regular sequences in the semigroup ring $R=\CC[K]$ of lattice points of the graded cone $K$. We conjecture that the quotients of $R$ by these sequences describe locally…

Homological Algebra of Mirror Symmetry

- Mathematics
- 1995

Mirror symmetry (MS) was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing…

On the $K$-theory of smooth toric DM stacks

- Mathematics
- 2005

We explicitly calculate the Grothendieck $K$-theory ring of a smooth toric Deligne-Mumford stack and define an analog of the Chern character. In addition, we calculate $K$-theory pushforwards and…