On the Chow groups of hypersurfaces in symplectic Grassmannians

TL;DR

This paper investigates the Chow groups of certain hypersurfaces in symplectic Grassmannians, demonstrating that many of these Chow groups inject into cohomology, thus linking algebraic cycles to topological invariants.

Contribution

It establishes injectivity of many Chow groups into cohomology for hypersurfaces in symplectic Grassmannians, a new insight in algebraic geometry.

Findings

Many Chow groups of the hypersurfaces inject into cohomology

The work applies to Plücker hypersurfaces in specific symplectic Grassmannians

Provides new connections between algebraic cycles and cohomological invariants

Abstract

Let $Y$ be a Pl\"ucker hypersurface in a symplectic Grassmannian $I_1 Gr(3,n)$ or a bisymplectic Grassmannian $I_2 Gr(3,n)$. We show that many Chow groups of $Y$ inject into cohomology.