Questions on the Chow ring of complete intersections
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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Geometry and complex manifolds
Publication details
- Journal / source
- Journal of the Mathematical Society of Japan
- Volume
- -1
- Issue
- -1
- Publication date
- 12 February 2026
- Language
- EN