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arXiv · 2011.10103

On curves with high multiplicity on $\mathbb{P}(a,b,c)$ for $\min(a,b,c)\leq4$

David McKinnon·Rindra Razafy·Matthew Satriano·Yuxuan Sun
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Abstract

On a weighted projective surface $\mathbb{P}(a,b,c)$ with $\min(a,b,c)\leq 4$, we compute lower bounds for the {\em effective threshold} of an ample divisor, in other words, the highest multiplicity a section of the divisor can have at a specified point. We expect that these bounds are close to being sharp. This translates into finding divisor classes on the blowup of $\mathbb{P}(a,b,c)$ that generate a cone contained in, and probably close to, the effective cone.

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David McKinnon, Rindra Razafy, Matthew Satriano, Yuxuan Sun. 2020-11-19. On curves with high multiplicity on $\mathbb{P}(a,b,c)$ for $\min(a,b,c)\leq4$. https://arxiv.org/abs/2011.10103

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