Vol. 11, No. 8, 2017

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Torsion orders of complete intersections

Andre Chatzistamatiou and Marc Levine

Vol. 11 (2017), No. 8, 1779–1835
Abstract

By a classical method due to Roitman, a complete intersection X of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer N, when viewed as a cycle in the Chow group, has support in X × D F × X, for some divisor D and a finite set of closed points F. The minimal such N is called the torsion order. We study lower bounds for the torsion order following the specialization method of Voisin, Colliot-Thélène, and Pirutka. We give a lower bound for the generic complete intersection with and without point. Moreover, we use methods of Kollár and Totaro to exhibit lower bounds for the very general complete intersection.

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Keywords
algebraic cycles, decomposition of the diagonal
Mathematical Subject Classification 2010
Primary: 14C25
Milestones
Received: 23 May 2016
Revised: 14 June 2017
Accepted: 29 July 2017
Published: 15 October 2017
Authors
Andre Chatzistamatiou
Fakultät Mathematik
Universität Duisburg-Essen
Essen
Germany
Marc Levine
Fakultät Mathematik
Universität Duisburg-Essen
Essen
Germany