Geodesic
Rigid divisors on surfaces
Izvestiya. Mathematics , Tome 84 (2020) no. 1, pp. 146-185.

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We study effective divisors $D$ on surfaces with $H^0(\mathcal{O}_D)=\Bbbk$ 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: negative divisors, rigid divisors, divisors on surfaces, spherelike sheaves. 
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A. Hochenegger; D. Ploog. Rigid divisors on surfaces. Izvestiya. Mathematics , Tome 84 (2020) no. 1, pp. 146-185. http://geodesic.mathdoc.fr/item/IM2_2020_84_1_a5/

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