Unobstructed Stanley-Reisner Degenerations for Dual Quotient Bundles on $G(2,n)$

TL;DR

This paper studies the algebraic and geometric properties of the dual quotient bundle on Grassmannians, showing its ideal has a special initial ideal and that its coordinate ring is rigid for large n.

Contribution

It proves the initial ideal of the dual quotient bundle's ideal is a Stanley-Reisner ideal of an unobstructed complex and establishes the rigidity of its coordinate ring for n>5.

Findings

Initial ideal equals a Stanley-Reisner ideal of an unobstructed complex

Coordinate ring has no infinitesimal deformations for n>5

Provides new insights into the algebraic structure of dual quotient bundles

Abstract

Let $Q^*$ denote the dual of the quotient bundle on the Grassmannian $G(2,n)$. We prove that the ideal of $Q^*$ in its natural embedding has initial ideal equal to the Stanley-Reisner ideal of a certain unobstructed simplicial complex. Furthermore, we show that the coordinate ring of $Q^*$ has no infinitesimal deformations for $n>5$.