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Stratifying Quotient Stacks and Moduli Stacks

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Geometry of Moduli (Abelsymposium 2017)

Part of the book series: Abel Symposia ((ABEL,volume 14))

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Abstract

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X∕H], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly on X, in such a way that each stratum [S∕H] has a geometric quotient S∕H. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.

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Acknowledgment

V.H. is supported by the Excellence Initiative of the DFG at the Freie Universität Berlin.

Author information

Authors and Affiliations

  1. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Gergely Bérczi

  2. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Victoria Hoskins

  3. Mathematical Institute, Oxford University, Oxford, UK

    Frances Kirwan

Authors
  1. Gergely Bérczi
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  2. Victoria Hoskins
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  3. Frances Kirwan
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Corresponding author

Correspondence to Frances Kirwan .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oslo, Oslo, Norway

    Jan Arthur Christophersen

  2. Department of Mathematics, University of Oslo, Oslo, Norway

    Kristian Ranestad

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Bérczi, G., Hoskins, V., Kirwan, F. (2018). Stratifying Quotient Stacks and Moduli Stacks. In: Christophersen, J., Ranestad, K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-94881-2_1

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