GIT of complete intersections and log canonical thresholds

TL;DR

This paper explores the relationship between GIT stability of complete intersections and their log canonical thresholds, providing new insights into their geometric and stability properties.

Contribution

It establishes a novel connection between GIT stability and log canonical thresholds for complete intersections and their variations.

Findings

Link between GIT stability and log canonical thresholds

Extension of results to Variations of GIT quotients

Framework for analyzing stability of complete intersections

Abstract

We establish a link between the GIT stability of complete intersections of same degree hypersurfaces in the same ambient projective space, which can be parametrised as tuples in a Grassmanian scheme, and the log canonical thresholds of hypersurfaces contained in these tuples. We also establish a similar link in the case of Variations of GIT quotients, where we consider tuples of complete intersections and distinct hyperplanes.