Bloch's conjecture for Enriques varieties

2017/06/19 by Robert Laterveer, Laterveer, Robert
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · doi:10.48550/arxiv.1706.05822

Abstract

Enriques varieties have been defined as higher-dimensional generalizations of Enriques surfaces. Bloch's conjecture implies that Enriques varieties should have trivial Chow group of zero-cycles. We prove this is the case for all known examples of irreducible Enriques varieties of index larger than 2. The proof is based on results concerning the Chow motive of generalized Kummer varieties.

Related

• Bloch's conjecture on certain surfaces of general type with p_g=0 and with an involution: the Enriques case
• Bloch's conjecture on surfaces of general type with p_g=q=0, K²=3 and with an involution
• Bloch's formula for 0-cycles with modulus and higher dimensional Class Field Theory
• Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties
• Bloch's conjecture for Inoue surfaces with p_g=0, K² =7