On stable rationality of some conic bundles and moduli spaces of Prym\n curves

2016/05/10 by Christian Böhning, Böhning, Christian, Hans‐Christian Graf von Bothmer +1 · 2 citations
Mathematics · #14E08 #14M20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1605.03029

openalex publication_date 2016/05/10 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We prove that a very general hypersurface of bidegree (2, n) in P² x P² for\nn bigger than or equal to 2 is not stably rational, using Voisin's method of\nintegral Chow-theoretic decompositions of the diagonal and their preservation\nunder mild degenerations. At the same time, we also analyse possible ways to\ndegenerate Prym curves, and the way how various loci inside the moduli space of\nstable Prym curves are nested. No deformation theory of stacks or sheaves of\nAzumaya algebras like in recent work of Hasset-Kresch-Tschinkel is used, rather\nwe employ a more elementary and explicit approach via Koszul complexes, which\nis enough to treat this special case.\n

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