Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Moduli of nodal curves on smooth surfaces of general type


Author: F. Flamini
Journal: J. Algebraic Geom. 11 (2002), 725-760
DOI: https://doi.org/10.1090/S1056-3911-02-00322-3
Published electronically: June 10, 2002
MathSciNet review: 1910265
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Abstract | References | Additional Information

Abstract: In this paper we focus on the problem of computing the number of moduli of the so called Severi varieties (denoted by $V_{\vert D \vert, \delta}$), which parametrize universal families of irreducible, $\delta$-nodal curves in a complete linear system $\vert D\vert$, on a smooth projective surface $S$ of general type. We determine geometrical and numerical conditions on $D$ and numerical conditions on $\delta$ ensuring that such a number coincides with $dim(V_{\vert D \vert, \delta})$. As related facts, we also determine some sharp results concerning the geometry of some Severi varieties.


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Additional Information

F. Flamini
Affiliation: Dipartimento di Matematica, Universita’ degli Studi di Roma - “Roma Tre", Largo San Leonardo Murialdo, 1 - 00146 Roma, Italy
Email: flamini@matrm3.mat.uniroma3.it

DOI: https://doi.org/10.1090/S1056-3911-02-00322-3
Received by editor(s): July 21, 2000
Published electronically: June 10, 2002
Additional Notes: The author is a member of GNSAGA-INdAM

American Mathematical Society