On the Chow Ring of Cynk-Hulek Calabi-Yau Varieties and Schreieder Varieties

Laterveer R, Vial C (2020)
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 72(2): 505-536.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Laterveer, Robert; Vial, CharlesUniBi
Abstract / Bemerkung
This note is about certain locally complete families of Calabi-Yau varieties constructed by Cynk and Hulek, and certain varieties constructed by Schreieder. We prove that the cyde class map on the Chow ring of powers of these varieties admits a section, and that these varieties admit a multiplicative self-dual Chow-Kunneth decomposition. As a consequence of both results, we prove that the subring of the Chow ring generated by divisors, Chern classes, and intersections of two cycles of positive codimension injects into cohomology via the cyde dass map. We also prove that the small diagonal of Schreieder surfaces admits a decomposition similar to that of K3 surfaces. As a by-product of our main result, we verify a conjecture of Voisin concerning zero-cycles on the self-product of Cynk-Hulek Calabi-Yau varieties, and in the odd-dimensional case we verify a conjecture of Voevodsky concerning smash-equivalence. Finally, in positive characteristic, we show that the supersingular Cynk-Hulek Calabi-Yau varieties provide examples of Calabi-Yau varieties with "degenerate" motive.
Stichworte
algebraic cycle; Chow ring; motive; Bloch-Beilinson filtration; multiplicative Chow-Kunneth decomposition; Calabi-Yau variety; supersingular variety
Erscheinungsjahr
2020
Zeitschriftentitel
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
Band
72
Ausgabe
2
Seite(n)
505-536
ISSN
0008-414X
eISSN
1496-4279
Page URI
https://pub.uni-bielefeld.de/record/2942901

Zitieren

Laterveer R, Vial C. On the Chow Ring of Cynk-Hulek Calabi-Yau Varieties and Schreieder Varieties. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. 2020;72(2):505-536.
Laterveer, R., & Vial, C. (2020). On the Chow Ring of Cynk-Hulek Calabi-Yau Varieties and Schreieder Varieties. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 72(2), 505-536. doi:10.4153/S0008414X19000191
Laterveer, R., and Vial, C. (2020). On the Chow Ring of Cynk-Hulek Calabi-Yau Varieties and Schreieder Varieties. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 72, 505-536.
Laterveer, R., & Vial, C., 2020. On the Chow Ring of Cynk-Hulek Calabi-Yau Varieties and Schreieder Varieties. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 72(2), p 505-536.
R. Laterveer and C. Vial, “On the Chow Ring of Cynk-Hulek Calabi-Yau Varieties and Schreieder Varieties”, CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, vol. 72, 2020, pp. 505-536.
Laterveer, R., Vial, C.: On the Chow Ring of Cynk-Hulek Calabi-Yau Varieties and Schreieder Varieties. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. 72, 505-536 (2020).
Laterveer, Robert, and Vial, Charles. “On the Chow Ring of Cynk-Hulek Calabi-Yau Varieties and Schreieder Varieties”. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 72.2 (2020): 505-536.

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