Rigid divisors on surfaces

Abstract

We study effective divisors $D$ on surfaces with $H^0({\mathcal{O}}_D)=k$ and $H^1({\mathcal{O}}_D)=H^0({\mathcal{O}}_D(D))=0$. We give a numerical criterion for such divisors, following a general investigation of negativity, rigidity and connectivity properties. Examples include exceptional loci of rational singularities, and spherelike divisors.

35 pages. Many changes, not all minor. Two major changes: (1) proof of Proposition 2.10 had a gap, replaced by Conjecture 2.10 (2) statement of Lemma 5.3 was incomplete, Section 5.1 rewritten. Same content as published version

References in corpus (3)

• Ultrametric spaces of branches on arborescent singularities
• Tilting chains of negative curves on rational surfaces
• Exceptional sequences and spherical modules for the Auslander algebra of $k[x]/(x^t)$

Cited by in corpus (1)

• Formality of $\mathbb{P}$-objects