A. Hochenegger, D. Ploog

Rigid Divisors on Surfaces

Izvestiya: Mathematics, 84(1):146-185, 2020.
DOI: 10.1070/IM8721

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.

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