Compactifying the space of stable maps
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This article is published in Journal of the American Mathematical Society.The article was published on 2001-07-31 and is currently open access. It has received 513 citations till now. The article focuses on the topics: Quaternionic projective space & Complex projective space.read more
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Gromov-Witten theory of Deligne-Mumford stacks
TL;DR: In this article, Gromov-Witten invariants of a smooth complex Deligne-Mumford stack with a projective coarse moduli space were introduced and proved.
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Orbifold Gromov-Witten Theory
Weimin Chen Chen,Yongbin Ruan +1 more
TL;DR: In this paper, the notion of good map was introduced and used to establish Gromov-Witten theory for orbifolds, and the good map theory was used to define good map.
Journal ArticleDOI
The Witten equation, mirror symmetry, and quantum singularity theory
TL;DR: In this paper, a family of moduli spaces, a virtual cycle, and a corresponding cohomological eld theory associated to the singularity are described for any nondegenerate, quasi-homogeneous hypersurface singularity.
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Twisted Bundles and Admissible Covers
TL;DR: In this article, the authors studied the structure of the stacks of twisted stable maps to the classifying stack of a finite group G, which they called the stack of twisted G-covers, or twisted g-bundles.
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Orbifolds and Stringy Topology
TL;DR: An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry, is given in this article, where a detailed description of the Chen-Ruan cohomology is provided.
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Éléments de géométrie algébrique
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
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Commutative Ring Theory
Hideyuki Matsumura,Miles Reid +1 more
TL;DR: In this article, the authors introduce the notion of complete local rings and apply it to a wide range of applications, including: I-smoothness, I-flatness revisited, and valuation rings.
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The irreducibility of the space of curves of given genus
Pierre Deligne,David Mumford +1 more
TL;DR: In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).
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Éléments de géométrie algébrique : III. Étude cohomologique des faisceaux cohérents, Seconde partie
TL;DR: In this paper, the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.html).