Free divisors in a pencil of curves

Jean Vallès

Note that erratum exists for this article.

Journal of Singularities
volume 11 (2015), 190-197

Received: 17 February 2015. Received in revised form: 26 June 2015.

DOI: 10.5427/jsing.2015.11h

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Abstract:

A plane curve D in P^2(k), where k is a field of characteristic zero, is free if its associated sheaf of vector fields tangent to D is a free module over the structure sheaf on P^2(k). Relatively few free curves are known. Here we prove that the union of all singular members of a pencil of plane projective curves with the same degree and with a smooth base locus is a free divisor.

Keywords:

Arrangements of curves, Pencil of curves, Freeness of arrangements, Logarithmic sheaves

Mathematical Subject Classification:

14C21, 14N20, 32S22, 14H50

Author(s) information:

Jean Vallès
Université de Pau et des Pays de l'Adour
Avenue de l'Université - BP 576
64012 PAU Cedex - France
email: jean.valles@univ-pau.fr