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Geometric Invariant Theory

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Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration

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Abstract

The purpose of Geometric Invariant Theory (abbreviated GIT) is to provide a way to define a quotient of an algebraic variety X by the action of a reductive complex algebraic group G with an algebro-geometric structure. In this chapter we present a sketch of the treatment with a variety of examples. We also review the notion of stability from the differential and symplectic points of view and explore the idea of maximal unstability.

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Authors and Affiliations

  1. Applied Mathematics, Technical University of Madrid, Madrid, Spain

    Alfonso Zamora Saiz

  2. School of Mathematics, University of Costa Rica, San José, Costa Rica

    Ronald A. Zúñiga-Rojas

Authors
  1. Alfonso Zamora Saiz
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  2. Ronald A. Zúñiga-Rojas
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Zamora Saiz, A., Zúñiga-Rojas, R.A. (2021). Geometric Invariant Theory. In: Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-67829-6_3

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