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Twisted Bundles and Admissible Covers
Abstract We study the structure of the stacks of twisted stable maps to the classifying stack of a finite group G—which we call the stack of twisted G-covers, or twisted G-bundles. For a suitable
A mirror theorem for toric stacks
We prove a Givental-style mirror theorem for toric Deligne–Mumford stacks ${\mathcal{X}}$. This determines the genus-zero Gromov–Witten invariants of ${\mathcal{X}}$ in terms of an explicit
G2-manifolds and associative submanifolds via semi-Fano 3-folds
We construct many new topological types of compact G_2-manifolds, i.e. Riemannian 7-manifolds with holonomy group G_2. To achieve this we extend the twisted connected sum construction first developed
Explicit birational geometry of 3-folds
Foreword 1. One parameter families containing three dimensional toric Gorenstein singularities K. Altmann 2. Nonrational covers of CPm x CPn J. Kollar 3. Essentials of the method of maximal
Computing genus-zero twisted Gromov-Witten invariants
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 and an invertible
Weighted Grassmannians
Many classes of projective algebraic varieties can be studied in terms of graded rings. Gorenstein graded rings in small codimension have been studied recently from an algebraic point of view, but
Quantum periods for 3-dimensional Fano manifolds
The quantum period of a variety X is a generating function for certain Gromov-Witten invariants of X which plays an important role in mirror symmetry. In this paper we compute the quantum periods of
Birational geometry of terminal quartic 3-folds, I
<abstract abstract-type="TeX"><p>In this paper, we study the birational geometry of certain examples of mildly singular quartic 3-folds. A quartic 3-fold is a special case of a Fano variety, that is,
Del Pezzo surfaces over Dedekind schemes
Let S be a Dedekind scheme with fraction field K. We study the following problem: given a Del Pezzo surface X, defined over K, construct a distinguished integral model of X, defined over all of S. We