Work

Questions on the Chow ring of complete intersections

Year: 2026

Type: article

Abstract: We state several questions, and prove some partial results, about the Chow ring $A^{\ast}(X)$ of complete intersections in projective space. For one thing, we prove that if $X$ is a general Calabi–Yau hypersurface, the intersection product $A^{2}(X) \cdot A^{i}(X)$ is one-dimensional, for any $i > 0$. We also show that quintic threefolds have a multiplicative Chow–Künneth (MCK) decomposition. We wonder whether all Calabi–Yau hypersurfaces might have an MCK decomposition, and prove this is the case conditional to a conjecture of Voisin.

Source: Journal of the Mathematical Society of Japan

DOI: 10.2969/jmsj/94569456

Author: Robert LATERVEER

Institutions: Centre National de la Recherche Scientifique, Institut de Recherche Mathématique Avancée, Université de Strasbourg

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: From Fano to hyperKähler varieties: geometry and derived categories