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Twisted Bundles and Admissible Covers
- D. Abramovich, A. Corti, Angelo Vistoli
- Mathematics
- 25 June 2001
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…
Explicit Birational Geometry of 3-Folds: Singularities of linear systems and 3-fold birational geometry
- A. Corti
- Mathematics
- 2000
A mirror theorem for toric stacks
- T. Coates, A. Corti, H. Iritani, Hsian-hua Tseng
- MathematicsCompositio Mathematica
- 15 October 2013
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
- A. Corti, M. Haskins, Johannes Nordstrom, T. Pacini
- Mathematics
- 18 July 2012
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
- T. Coates, A. Corti, H. Iritani, Hsian-hua Tseng
- Mathematics
- 8 February 2007
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
- T. Coates, A. Corti, Sergey Galkin, A. Kasprzyk
- Mathematics
- 13 March 2013
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
- A. Corti
- Mathematics
- 31 May 1995
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…
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