A theorem on zero cycles on surfaces

Authors

  • Rina Roxana Paucar Rojas Instituto de Matemáticas y Ciencias Afines, Universidad Nacional de Ingeneria, Lima, Perú.
  • Claudia Schoemann Laboratoire Gaati, Université de la Polynésie Francaise, Papeete, French Polynesia.

DOI:

https://doi.org/10.17268/sel.mat.2022.01.13

Keywords:

Zero-cycles, Chow groups, surfaces, constant cycle curves, general type surface

Abstract

In this paper we prove a result on 0-cycles on surfaces as an application of the theorem on the kernel of the Gysin homomorphism of Chow groups of 0-cycles of degree zero induced by the embedding of a curve into a surface, and we study the connection of this result with Bloch’s conjecture and constant cycles curves.

References

Voisin C. Hodge Theory and Complex Algebraic Geometry II: Volume 2. Paris: Cambridge University Press, 2003.

Voisin C. Hodge Theory and Complex Algebraic Geometry I: Volume 1. Paris: Cambridge University Press, 2002.

Huybrechts D, et al. Curves and cycles on k3 surfaces. arXiv preprint arXiv:1303.4564, 2013.

Roitman AA. Rational equivalence of zero-cycles. Mathematics of the USSR- Sbornik. 1972; 18(4):571.

Paucar R, Schoemann C. On the kernel of the Gysin homomorphism on Chow groups of zero cycles. Submitted at Publications Mathématiques de Besancon for the Post-proceedings issue of the GTA conference in Papeete–Faaa, French-Polynesia. 2021; 16-20 August 2021 (submitted 30.11.2021).

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Published

2022-07-27

How to Cite

Paucar Rojas, R. R., & Schoemann, C. (2022). A theorem on zero cycles on surfaces. Selecciones Matemáticas, 9(01), 161 - 166. https://doi.org/10.17268/sel.mat.2022.01.13

Issue

Vol. 9 No. 01 (2022): January - July

Section

Articles

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