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On stable rationality of some conic bundles and moduli spaces of Prym curves
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Böhning, Christian and Bothmer, Hans-Christian Graf von (2017) On stable rationality of some conic bundles and moduli spaces of Prym curves. Commentarii Mathematici Helvetici, 93 (1). pp. 133-155. doi:10.4171/CMH/431 ISSN 0010-2571.
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Official URL: https://doi.org/10.4171/CMH/431
Abstract
We prove that a very general hypersurface of bidegree (2, n) in P 2 × P 2 for n bigger than or equal to 2 is not stably rational, using Voisin’s method of integral Chow-theoretic decompositions of the diagonal and their preservation under mild degenerations. At the same time, we also analyse possible ways to degenerate Prym curves, and the way how various loci inside the moduli space of stable Prym curves are nested. No deformation theory of stacks or sheaves of Azumaya algebras like in recent work of Hassett-Kresch-Tschinkel is used, rather we employ a more elementary and explicit approach via Koszul complexes, which is enough to treat this special case.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Abelian varieties, Curves, Algebraic, Morphisms (Mathematics) | ||||||
Journal or Publication Title: | Commentarii Mathematici Helvetici | ||||||
Publisher: | European Mathematical Society Publishing House | ||||||
ISSN: | 0010-2571 | ||||||
Official Date: | 3 September 2017 | ||||||
Dates: |
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Volume: | 93 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 133-155 | ||||||
DOI: | 10.4171/CMH/431 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 13 January 2017 | ||||||
Date of first compliant Open Access: | 13 January 2017 | ||||||
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