Rigid divisors on surfaces

Andreas Hochenegger; David Ploog

doi:10.1070/IM8721

Rigid divisors on surfaces

Algebraic Geometry 2020-03-24 v2

Authors: Andreas Hochenegger , David Ploog

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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.

Keywords

del pezzo surfaces algebraic surfaces

Cite

@article{arxiv.1607.08198,
  title  = {Rigid divisors on surfaces},
  author = {Andreas Hochenegger and David Ploog},
  journal= {arXiv preprint arXiv:1607.08198},
  year   = {2020}
}

Comments

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

Rigid divisors on surfaces

Abstract

Keywords

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