Kyoto Journal of Mathematics

Algebraic cycles and Todorov surfaces

Robert Laterveer

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Abstract

Motivated by the Bloch–Beilinson conjectures, Voisin has formulated a conjecture about 0-cycles on self-products of surfaces of geometric genus one. We verify Voisin’s conjecture for the family of Todorov surfaces with K2=2 and fundamental group Z/2Z. As a by-product, we prove that certain Todorov surfaces have finite-dimensional motive.

Article information

Source
Kyoto J. Math., Volume 58, Number 3 (2018), 493-527.

Dates
Received: 21 December 2015
Revised: 6 July 2016
Accepted: 30 September 2016
First available in Project Euclid: 20 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1529481671

Digital Object Identifier
doi:10.1215/21562261-2017-0027

Mathematical Reviews number (MathSciNet)
MR3843388

Zentralblatt MATH identifier
06959089

Subjects
Primary: 14C15: (Equivariant) Chow groups and rings; motives
Secondary: 14C25: Algebraic cycles 14C30: Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture 14J28: $K3$ surfaces and Enriques surfaces 14J29: Surfaces of general type

Keywords
Algebraic cycles Chow groups motives finite-dimensional motives surfaces of general type Todorov surfaces K3 surfaces

Citation

Laterveer, Robert. Algebraic cycles and Todorov surfaces. Kyoto J. Math. 58 (2018), no. 3, 493--527. doi:10.1215/21562261-2017-0027. https://projecteuclid.org/euclid.kjm/1529481671


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