Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book
covers the standard topics in toric geometry; a novel feature is that each of the first nine …

We show that the skeleton of the Deligne-Mumford-Knudsen moduli stack of stable curves is
naturally identified with the moduli space of extended tropical curves, and that this is …

We introduce an integral structure in orbifold quantum cohomology associated to the K-
group and the Γˆ-class. In the case of compact toric orbifolds, we show that this integral …

We construct new supersymmetric AdS 2× M 4 solutions of D= 6 gauged supergravity, where
M 4 are certain four-dimensional orbifolds. After uplifting to massive type IIA supergravity …

Equivariant cohomology has become an indispensable tool in algebraic geometry and in
related areas including representation theory, combinatorial and enumerative geometry, and …

We study the relationship between derived categories of factorizations on gauged Landau–
Ginzburg models related by variations of the linearization in Geometric Invariant Theory …

Given a vector bundle F on a smooth Deligne–Mumford stack X and an invertible
multiplicative characteristic class c, we define orbifold Gromov–Witten invariants of X twisted …

Abstract Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of
stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X …

We give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a
“torus”. We show that our definition is equivalent to the one of Borisov, Chen and Smith in …

In this paper, we will discuss gauged linear sigma model descriptions of toric stacks. Toric
stacks have a simple description in terms of (symplectic, GIT) \bfC^* quotients of …