Remarks on the positivity of the cotangent bundle of an Enriques surface

Abstract

Let $S$ be an Enriques surface. In this paper we study the semistability of the restriction $Ω_{S}|_C$ for a general curve $C \in |H|$, where $H$ is a globally generated and ample line bundle on $S$. We show that $Ω_{S}|_C$ is semistable when $H^2 \ge 6$, or when $H^2 \ge 2$ and $S$ is very general. Moreover, we give explicit constructions of families of smooth irreducible curves that destabilize $Ω_S$.

Theorems & Definitions (11)

• Definition 2.1
• Theorem 2.2
• Theorem 2.3
• proof
• Lemma 2.4
• proof
• Proposition 2.5
• proof
• Remark 2.6
• Corollary 2.7