Semistability of logarithmic cotangent bundle on some projective manifolds

TL;DR

This paper studies the semistability of logarithmic cotangent bundles on certain smooth projective varieties, providing new results for log Del Pezzo surfaces, log Fano threefolds, and higher-dimensional cases with Picard number one.

Contribution

It establishes semistability conditions for logarithmic cotangent bundles on specific classes of projective manifolds, extending known results to new cases with Picard number one.

Findings

Semistability results for log Del Pezzo surfaces

Semistability for log Fano threefolds

Extension to log Fano n-folds with n ≤ 6

Abstract

In this paper, we investigate the semistability of logarithmic de Rham sheaves on a smooth projective variety, under suitable conditions. In particular when the Picard number is one, we obtain results for any log Del Pezzo surface, log Fano threefolds, and for log Fano $n$-folds of dimension $n\leq 6$.