Vector bundles on genus 2 curves and trivectors
- Creators
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Rains, Eric M.1
- Sam, Steven V.2
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1.
California Institute of Technology
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2.
University of Wisconsin–Madison
Abstract
Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic. Some of the aspects of this are known to be related to the geometric
invariant theory of the third exterior power of a 9-dimensional complex vector space. We extend this relationship to arbitrary fields and study some of the connections to invariant theory, which will be studied more in-depth in a followup paper.
Copyright and License
This journal is © Foundation Compositio Mathematica 2019. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited. For commercial re-use, please contact the Foundation Compositio Mathematica.
Acknowledgement
Steven V Sam was partially supported by a Miller research fellowship and NSF DMS-1500069.
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Additional details
- Miller Institute for Basic Research in Science
- National Science Foundation
- DMS-1500069
- Accepted
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2018-01-22
- Caltech groups
- Division of Physics, Mathematics and Astronomy (PMA)
- Publication Status
- Published