English

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

Algebraic Geometry 2020-11-23 v1

Abstract

On a weighted projective surface P(a,b,c)\mathbb{P}(a,b,c) with min(a,b,c)4\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 P(a,b,c)\mathbb{P}(a,b,c) that generate a cone contained in, and probably close to, the effective cone.

Keywords

Cite

@article{arxiv.2011.10103,
  title  = {On curves with high multiplicity on $\mathbb{P}(a,b,c)$ for $\min(a,b,c)\leq4$},
  author = {David McKinnon and Rindra Razafy and Matthew Satriano and Yuxuan Sun},
  journal= {arXiv preprint arXiv:2011.10103},
  year   = {2020}
}