ON THE RATIONALITY PROBLEM FOR QUADRIC BUNDLES

Schreieder, Stefan (2019): ON THE RATIONALITY PROBLEM FOR QUADRIC BUNDLES. In: Duke Mathematical Journal, Bd. 168, Nr. 2: S. 187-223

Abstract

We classify all positive integers n and r such that (stably) nonrational complex r - fold quadric bundles over rational n-folds exist. We show in particular that, for any n and r, a wide class of smooth r -fold quadric bundles over P-C(n) are not stably rational if r is an element of [2(n-1) - 1, 2(n) - 2]. In our proofs we introduce a generalization of the specialization method of Voisin and of Colliot-Thelene and Pirutka which avoids universally CH0-trivial resolutions of singularities.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0012-7094
• Sprache: Englisch