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2015 | OriginalPaper | Chapter

Introduction to Donaldson–Thomas and Stable Pair Invariants

Author: Michel van Garrel

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

Publisher: Springer New York

Abstract

This chapter is intended for the reader unaccostumed to sheaf counting theories and is meant to serve as a first introduction to Donaldson-Thomas and Stable Pair invariants. We elaborate on some aspects of the expostion in the survey paper by Pandharipande-Thomas. Our emphasis is on one hand on examples that illustrate the properties of the relevant moduli spaces, on the other hand on discussing some of the highlights of the theory.

previous chapter Introduction to Gromov–Witten Theory

next chapter Donaldson–Thomas Invariants and Wall-Crossing Formulas

We refer the reader to the appendix of [8] for a discussion of virtual classes.

Behrend, K.: Donaldson-Thomas invariants via microlocal geometry. Ann. Math. 170, 1307–1338 (2009) MathSciNetCrossRef

Behrend, K., Fantechi, B.: Symmetric obstruction theories and Hilbert schemes of points on threefolds. Algebra Number Theory 2, 313–345 (2008) MathSciNetCrossRefMATH

Bridgeland, T.: Hall algebras and curve-counting invariants. J. AMS 24, 969–998 (2011) MathSciNet

Levine, M., Pandharipande, R.: Algebraic cobordism revisited. Invent. Math. 176, 63–130 (2009) MathSciNetCrossRef

Li, J.: Zero dimensional Donaldson-Thomas invariants of threefolds. Geom. Topol. 10, 2117–2171 (2006) MathSciNetCrossRef

Maulik, D., Nekrasov, N., Okounkov, A., Pandharipande, R.: Gromov-Witten theory and Donaldson-Thomas theory I. Compos. Math. 142, 1263–1285 (2006) MathSciNetCrossRefMATH

Pandharipande, R., Thomas, R.P.: Curve counting via stable pairs in the derived category. Invent. Math. 178, 407–447 (2009) MathSciNetCrossRefMATH

Pandharipande, R., Thomas, R.P.: 13/2 ways of counting curves (2012). arXiv:1111.1552

Stoppa, J., Thomas, R.P.: Hilbert schemes and stable pairs: GIT and derived category wall crossings. Bull. SMF 139(3), 297–339 (2011) MathSciNet

10.

Thomas, R.P.: A holomorphic Cassons invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations. J. Differ. Geom. 54, 367–438 (2000)

11.

Toda, Y.: Curve counting theories via stable objects I: DT/PT correspondence. J. AMS 23, 1119–1157 (2010) MathSciNet

Title: Introduction to Donaldson–Thomas and Stable Pair Invariants
Author: Michel van Garrel
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_9

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Introduction to Donaldson–Thomas and Stable Pair Invariants

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