## 48 Citations

The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks

- Mathematics
- 2009

We extend our previous work arXiv:1007.0053 on coherent-constructible correspondence for toric varieties to include toric Deligne-Mumford (DM) stacks. Following Borisov-Chen-Smith, a toric DM stack…

Homological mirror symmetry for An-resolutions as a T-duality

- Mathematics, Computer ScienceJ. Lond. Math. Soc.
- 2013

A geometric functor is constructed from a derived Fukaya category of $\check{X}$ to the derived category of coherent sheaves on $X$ and it is shown that this is an equivalence of triangulation categories onto a full triangulated subcategory of $D^b(X)$, thus realizing Kontsevich's HMS conjecture by SYZ.

Homological mirror symmetry for log Calabi-Yau surfaces

- Mathematics
- 2020

Given a log Calabi-Yau surface $Y$ with maximal boundary $D$ and distinguished complex structure, we explain how to construct a mirror Lefschetz fibration $w: M \to \mathbb{C}$, where $M$ is a…

A categorification of Morelli’s theorem

- Mathematics
- 2010

We prove a theorem relating torus-equivariant coherent sheaves on toric varieties to polyhedrally-constructible sheaves on a vector space. At the level of K-theory, the theorem recovers Morelli’s…

Variation of GIT and Variation of Lagrangian Skeletons II: Quasi-Symmetric Case

- Mathematics
- 2020

Consider $(\mathbb{C}^*)^k$ acting on $\mathbb{C}^N$ satisfying certain 'quasi-symmetric' condition which produces a class of toric Calabi-Yau GIT quotient stacks. Using subcategories of…

Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space

- Mathematics
- 2012

We prove Homological Mirror Symmetry for a smooth $$d$$d-dimensional Calabi–Yau hypersurface in projective space, for any $$d \ge 3$$d≥3 (for example, $$d=3$$d=3 is the quintic threefold). The main…

Scattering diagrams from asymptotic analysis on Maurer–Cartan equations

- Mathematics, PhysicsJournal of the European Mathematical Society
- 2021

We investigate SYZ mirror symmetry via asymptotic analysis on Maurer-Cartan equations, following a program set forth by Fukaya. Let $X_0$ and $\check{X}_0$ be a mirror pair of semi-flat Calabi-Yau…

Variation of GIT and Variation of Lagrangian Skeletons I: Flip and Flop

- Mathematics
- 2020

Coherent-Constructible Correspondence for toric variety assigns to each $n$-dimensional toric variety $X_\Sigma$ a Lagrangian skeleton $\Lambda_\Sigma \subset T^*T^n$, such that the derived category…

Lagrangian skeleta of hypersurfaces in $$({\mathbb {C}}^*)^n$$

- Mathematics
- 2018

Let $W(z_1, \cdots, z_n): (\mathbb{C}^*)^n \to \mathbb{C}$ be a Laurent polynomial in $n$ variables, and let $\mathcal{H}$ be a generic smooth fiber of $W$. In \cite{RSTZ}…

On the homological mirror symmetry conjecture for pairs of pants

- Mathematics
- 2010

The n-dimensional pair of pants is defined to be the complement of n+2 generic hyperplanes in CP^n. We construct an immersed Lagrangian sphere in the pair of pants and compute its endomorphism…

## References

SHOWING 1-10 OF 48 REFERENCES

Homological mirror symmetry is T-duality for $\mathbb P^n$

- Mathematics
- 2008

In this paper, we apply the idea of T-duality to projective spaces. From a connection on a line bundle on $\mathbb P^n$, a Lagrangian in the mirror Landau-Ginzburg model is constructed. Under this…

Constructible sheaves and the Fukaya category

- Mathematics
- 2006

Let $X$ be a compact real analytic manifold, and let $T^*X$ be its cotangent bundle. Let $Sh(X)$ be the triangulated dg category of bounded, constructible complexes of sheaves on $X$. In this paper,…

A categorification of Morelli’s theorem

- Mathematics
- 2010

We prove a theorem relating torus-equivariant coherent sheaves on toric varieties to polyhedrally-constructible sheaves on a vector space. At the level of K-theory, the theorem recovers Morelli’s…

Mirror symmetry for weighted projective planes and their noncommutative deformations

- Mathematics
- 2004

We study the derived categories of coherent sheaves of weighted projective spaces and their noncommutative deformations, and the derived categories of Lagrangian vanishing cycles of their mirror…

Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds

- Mathematics, Physics
- 2003

In this paper, we first provide an explicit description of {\it all} holomorphic discs (``disc instantons'') attached to Lagrangian torus fibers of arbitrary compact toric manifolds, and prove their…

Homological Algebra of Mirror Symmetry

- Mathematics, Physics
- 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…

Microlocal branes are constructible sheaves

- Mathematics
- 2006

Let X be a compact real analytic manifold, and let T* X be its cotangent bundle. In a recent paper with Zaslow (J Am Math Soc 22:233–286, 2009), we showed that the dg category Shc(X) of constructible…

The classification of triangulated subcategories

- Mathematics
- 1997

The first main result of this paper is a bijective correspondence between the strictly full triangulated subcategories dense in a given triangulated category and the subgroups of its Grothendieck…

Characteristic cycles of constructible sheaves

- Mathematics
- 1996

In his paper [K], Kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds: let X be a real analytic manifold, and F a complex of sheaves of…

Geometric categories and o-minimal structures

- Mathematics
- 1996

The theory of subanalytic sets is an excellent tool in various analytic-geometric contexts; see, for example, Bierstone and Milman [1]. Regrettably, certain “nice” sets—like { (x, x) : x > 0 } for…