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arXiv · 2101.01756

Stability of pencils of plane curves, log canonical thresholds and multiplicities

Aline Zanardini
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Abstract

In this paper we study the problem of classifying pencils of curves of degree $d$ in $\mathbb{P}^2$ using geometric invariant theory. We consider the action of $SL(3)$ and we relate the stability of a pencil to the stability of its generators, to the log canonical threshold of its members, and to the multiplicities of its base points, thus obtaining explicit stability criteria.

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Aline Zanardini. 2021-01-05. Stability of pencils of plane curves, log canonical thresholds and multiplicities. https://doi.org/10.1007/s00209-021-02857-w

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