A note on a Griffiths-type ring for complete intersections in Grassmannians

TL;DR

This paper introduces a Griffiths-type ring for smooth complete intersections in Grassmannians, enabling explicit computation of their Hodge groups, analogous to the classical Jacobian ring in projective space.

Contribution

It defines a new Griffiths-type ring for complete intersections in Grassmannians, extending classical methods to a broader geometric setting.

Findings

Explicit computation of Hodge groups for these intersections

Establishment of the Griffiths-type ring as an effective tool

Analogy with classical Jacobian rings in projective space

Abstract

We calculate a Griffiths-type ring for smooth complete intersection in Grassmannians. This is the analogue of the classical Jacobian ring for complete intersections in projective space, and allows us to explicitly compute their Hodge groups.