Proceedings of the American Mathematical Society

Author(s): Tomasz Szemberg; Halszka Tutaj-Gasinska
Journal: Proc. Amer. Math. Soc. 130 (2002), 2515-2524.
MSC (2000): Primary 14E25; Secondary 14C20
Posted: April 22, 2002
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Abstract: We study linear series on a projective plane blown up in a bunch of general points. Such series arise from plane curves of fixed degree with assigned fat base points. We give conditions (expressed as inequalities involving the number of points and the degree of the plane curves) on these series to be base point free, i.e. to define a morphism to a projective space. We also provide conditions for the morphism to be a higher order embedding. In the discussion of the optimality of obtained results we relate them to the Nagata Conjecture expressed in the language of Seshadri constants and we give a lower bound on these invariants.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14E25, 14C20

Tomasz Szemberg
Affiliation: Instytut Matematyki, Uniwersytet Jagiellonski, Reymonta 4, PL-30-059 Kraków, Poland
Address at time of publication: Universität GH Essen, FB 6 Mathematik, D-45117 Essen, Germany
Email: szemberg@im.uj.edu.pl

Halszka Tutaj-Gasinska
Affiliation: Instytut Matematyki, Uniwersytet Jagiellonski, Reymonta 4, PL-30-059 Kraków, Poland
Email: htutaj@im.uj.edu.pl

DOI: 10.1090/S0002-9939-02-06488-2
PII: S 0002-9939(02)06488-2
Received by editor(s): October 13, 2000
Received by editor(s) in revised form: March 30, 2001
Posted: April 22, 2002
Additional Notes: The first author was partially supported by KBN grant 2 P03A 00816.
The second author was partially supported by KBN grant 2 P03A 01418.
Communicated by: Michael Stillman
Copyright of article: Copyright 2002, American Mathematical Society

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