Geodesic
Free divisors in a pencil of curves
Journal of Singularities, Tome 11 (2015), pp. 190-197

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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.
DOI : 10.5427/jsing.2015.11h
Classification : 14C21, 14N20, 32S22, 14H50 
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     author = {Jean Vall\`es},
     title = {Free divisors in a pencil of curves},
     journal = {Journal of Singularities},
     pages = {190--197},
     publisher = {mathdoc},
     volume = {11},
     year = {2015},
     doi = {10.5427/jsing.2015.11h},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2015.11h/}
}
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Jean Vallès. Free divisors in a pencil of curves. Journal of Singularities, Tome 11 (2015), pp. 190-197. doi: 10.5427/jsing.2015.11h

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