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2015 | OriginalPaper | Chapter

Introduction to Donaldson–Thomas and Stable Pair Invariants

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Author: Michel van Garrel

Publisher: Springer New York

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

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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.

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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

Book

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

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

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

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

DOI

https://doi.org/10.1007/978-1-4939-2830-9_9

Author:

Michel van Garrel

Publisher

Springer New York

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