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

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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
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:	Date Event 3 September 2017 Published 9 January 2017 Accepted
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
Related URLs:	Publisher

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