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arXiv · 2609.06845

Polynomial Lower Bounds for Anticanonical Volumes of Weak Fano Surfaces

Pinxian Bie
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Abstract

We prove an explicit lower bound of order $\varepsilon^3/(1+\log(1/\varepsilon))$ for the anticanonical volume of every complex $\varepsilon$-log canonical weak del Pezzo surface. This general estimate is close to being sharp, as it differs from the conjectured optimal quadratic order only by one power of $\varepsilon$ and a logarithmic factor.

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Pinxian Bie. 2026-09-06. Polynomial Lower Bounds for Anticanonical Volumes of Weak Fano Surfaces. https://arxiv.org/abs/2609.06845

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