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General blow-ups of the projective plane

Authors: Tomasz Szemberg and Halszka Tutaj-Gasinska
Journal: Proc. Amer. Math. Soc. 130 (2002), 2515-2524
MSC (2000): Primary 14E25; Secondary 14C20
Published electronically: April 22, 2002
MathSciNet review: 1900857
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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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Additional Information

Tomasz Szemberg
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, PL-30-059 Kraków, Poland
Address at time of publication: Universität GH Essen, FB 6 Mathematik, D-45117 Essen, Germany

Halszka Tutaj-Gasinska
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, PL-30-059 Kraków, Poland

Received by editor(s): October 13, 2000
Received by editor(s) in revised form: March 30, 2001
Published electronically: 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
Article copyright: © Copyright 2002 American Mathematical Society

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