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2015 | OriginalPaper | Chapter

Introduction to Gromov–Witten Theory

Author: Simon C. F. Rose

Published in: Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Publisher: Springer New York

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Abstract

The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk given at the Fields Institute during a week-long conference aimed at introducing graduate students to the subject which took place during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics.
previous chapter Mirror Symmetry in Physics: The Basics
next chapter Introduction to Donaldson–Thomas and Stable Pair Invariants
Footnotes
1
The best way to define this is as a category whose objects are flat families of stable maps, and whose morphisms are commutative cartesian diagrams. That this is a category is reasonably clear; that it is any sort of “space” is far less so. However, many of the other structures described below become fairly clear in this context. For good references (admittedly, in the orbifold setting), see [1, 2, 5].
 
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Abramovich, D., Graber, T., Vistoli, A.: Gromov-Witten theory of Deligne-Mumford stacks. Am. J. Math. 130(5), 1337–1398 (2008). MR 2450211 (2009k:14108)
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Behrend, K., Fantechi, B.: The intrinsic normal cone. Invent. Math. 128(1), 45–88 (1997). MR 1437495 (98e:14022)
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Cox, D., Katz, S.: Mirror Symmetry and Algebraic Geometry, ch. 7. American Mathematical Society, Providence (1999)
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Gillam, W.: Hyperelliptic Gromov-Witten theory. Ph.D. thesis, Columbia University (2008)
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Hirzebruch, F.: Topological Methods in Algebraic Geometry. Springer, Berlin/New York (1995) MATH
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Knudsen, F.F.: The projectivity of the moduli space of stable curves. II. The stacks M g, n . Math. Scand. 52(2), 161–199 (1983). MR 702953 (85d:14038a)
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Okounkov, A., Pandharipande, R.: Gromov-Witten theory, hurwitz theory, and completed cycles. Anal. Math. 163(2), 517–560 (2006) MathSciNetMATH
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Pandharipande, R., Thomas, R.: 13/2 ways of counting curves. In: Proceedings of School on Moduli Spaces, Cambridge. London Mathematical Society Lecture Notes Series, vol. 411, pp. 282–333. Cambridge University Press, Cambridge (2014). MR 3221298
Metadata
Title
Introduction to Gromov–Witten Theory
Author
Simon C. F. Rose
Copyright Year
2015
Publisher
Springer New York
Book
Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Print ISBN: 978-1-4939-2829-3

Electronic ISBN: 978-1-4939-2830-9

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-1-4939-2830-9_8

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