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.
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.
Arrangements of curves, Pencil of curves, Freeness of arrangements, Logarithmic sheaves
Mathematical Subject Classification:
14C21, 14N20, 32S22, 14H50
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