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arXiv · 2603.27596

Numerical inequalities for quasi-projective surfaces

Rita Pardini·Sofia Tirabassi
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Abstract

Let $V$ be a smooth quasi-projective complex surface with compactification $(X,D)$ and set $\overline P_1(V):=h^0(X,K_X+D)$, $\overline q(V):=h^0(X,\Omega^1_X(\log D))$. We prove that $\overline P_1(V)\ge \overline q(V)-1$ if $V$ has maximal Albanese dimension and $\overline P_1(V)\ge\frac 16( \overline q(V)-5)$ otherwise. Both bounds are sharp.

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Rita Pardini, Sofia Tirabassi. 2026-03-29. Numerical inequalities for quasi-projective surfaces. https://arxiv.org/abs/2603.27596

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