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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.