SOME RESULTS OF REGULARITY FOR SEVERI VARIETIES OF PROJECTIVE SURFACES

Abstract

For a linear system |C| on a smooth projective surface S, whose general member is a smooth, irreducible curve, the Severi variety V |C|,δ is the locally closed subscheme of |C| which parametrizes curves with only δ nodes as singularities. In this paper we give numerical conditions on the class of divisors and upper bounds on δ, ensuring that the corresponding Severi variety is smooth of codimension δ, Our result generalizes what is proven in [7] and [10]. We also consider examples of smooth Severi varieties on surfaces of general type in P 3 which contain a line. The author is a member of GNSAGA-CNR.