Positivity of tangent bundle of weak Del Pezzo surfaces of degree $4$

TL;DR

This paper proves that the tangent bundle of weak Del Pezzo surfaces of degree at least 4 is almost nef, using total dual VMRTs from conic bundle structures.

Contribution

It establishes the almost nef property of tangent bundles for a class of weak Del Pezzo surfaces, a new result in algebraic geometry.

Findings

Tangent bundle of weak Del Pezzo surfaces of degree ≥ 4 is almost nef.

Uses total dual VMRTs induced by conic bundle structures.

Provides a new approach to studying tangent bundles of algebraic surfaces.

Abstract

In this paper, we prove that for any weak Del Pezzo surface $S$ of degree at least $4$, the tangent bundle $T_S$ is almost nef. For the proof, we use total dual VMRTs induced by conic bundle structures.