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arXiv · 2410.13543

Limit canonical series

Omid Amini·Eduardo Esteves·Eduardo Garcez
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Abstract

We describe the limits of canonical series along families of curves degenerating to a nodal curve which is general for its topology, in the weak sense that the branches over nodes on each of its components are in general position. We define a fan structure on the space of edge lengths on the dual graph of the limit curve, and construct a projective variety parametrizing the limits, organized in strata associated to the cones of this fan. This extends to all topologies the works by Eisenbud-Harris (Invent. Math. 87: 496-515, 1987) on curves of compact type and Esteves-Medeiros (Invent. Math. 149: 267-338, 2002) on two-component curves.

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Omid Amini, Eduardo Esteves, Eduardo Garcez. 2024-10-17. Limit canonical series. https://arxiv.org/abs/2410.13543

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