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

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.

11 pages

Cited by in corpus (1)

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