Abstract:
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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