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Geometric Representation Theory and Gauge Theory pp 53–81Cite as

Moduli Spaces of Sheaves on Surfaces: Hecke Correspondences and Representation Theory

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Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2248))

Abstract

In modern terms, enumerative geometry is the study of moduli spaces: instead of counting various geometric objects, one describes the set of such objects, which if lucky enough to enjoy good geometric properties is called a moduli space. For example, the moduli space of linear subspaces of \({\mathbb {A}}^n\) is the Grassmannian variety, which is a classical object in representation theory. Its cohomology and intersection theory (as well as those of its more complicated cousins, the flag varieties) have long been studied in connection with the Lie algebras \(\mathfrak {sl}_n\).

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Acknowledgements

I would like to thank the organizers of the CIME School on Geometric Representation Theory and Gauge Theory: Ugo Bruzzo, Antonella Grassi and Francesco Sala, for making this wonderful event possible. Special thanks are due to Davesh Maulik and Francesco Sala for all their support along the way. I would like to thank the referee for their wonderful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Andrei Neguţ

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  1. Andrei Neguţ
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Correspondence to Andrei Neguţ .

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Editors and Affiliations

  1. Department of Mathematics, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy

    Ugo Bruzzo

  2. Department of Mathematics, Università di Bologna, Bologna, Italy

    Antonella Grassi

  3. Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, University of Tokyo, Kashiwa-shi, Chiba, Japan

    Francesco Sala

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Neguţ, A. (2019). Moduli Spaces of Sheaves on Surfaces: Hecke Correspondences and Representation Theory. In: Bruzzo, U., Grassi, A., Sala, F. (eds) Geometric Representation Theory and Gauge Theory. Lecture Notes in Mathematics(), vol 2248. Springer, Cham. https://doi.org/10.1007/978-3-030-26856-5_2

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