Canonical blow-ups of Grassmannians II

TL;DR

This paper presents a linear algebraic construction of Lafforgue spaces related to Grassmannians by blowing up specific monomial ideals, leading to new compactifications with applications to high-complexity homogeneous varieties.

Contribution

It introduces a novel linear algebraic method for constructing Lafforgue spaces of Grassmannians, extending previous results and providing new compactifications in non-spherical settings.

Findings

Construction of Lafforgue spaces via blow-ups of monomial ideals

New examples of high-complexity homogeneous varieties with compactifications

Generalization of Faltings' results on Grassmannian-related spaces

Abstract

We give a linear algebraic construction of the Lafforgue spaces associated to the Grassmannians $G(2,n)$ by blowing up certain explicitly defined monomial ideals, which sharpens and generalizes a result of Faltings. As an application, we provide a family of homogeneous varieties with high complexity and with nice compactifications, which exhibits the notion of homeward compactification introduced in our previous work in a non-spherical setting.