Symmetric correspondences on quadrics

TL;DR

This paper investigates the relationship between the rationality of algebraic cycles on orthogonal grassmannians and those on fiber products of quadrics, providing new insights into their algebraic properties.

Contribution

It establishes a comparison result linking the rationality of algebraic cycles on orthogonal grassmannians with that on fiber products of quadrics, advancing understanding in algebraic geometry.

Findings

Proves a comparison theorem for algebraic cycle rationality

Connects rationality properties between grassmannians and quadrics

Enhances understanding of algebraic cycles on quadrics

Abstract

We prove a result comparing the rationality of some elementary algebraic cycles introduced by Alexander Vishik, defined on orthogonal grassmannians, with the rationality of some algebraic cycles defined on fiber products of the corresponding quadric.