Higher order embeddings of certain blow-ups of

Authors:
Cindy De Volder and Halszka Tutaj-Gasinska

Journal:
Proc. Amer. Math. Soc. **137** (2009), 4089-4097

MSC (2000):
Primary 14C20

DOI:
https://doi.org/10.1090/S0002-9939-09-10037-0

Published electronically:
July 10, 2009

MathSciNet review:
2538570

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be the blow-up of the projective plane along general points of a smooth cubic plane curve and let be the linear series of strict transforms of plane curves of degree having multiplicity at least at the -th blown-up point. We prove that if is -very ample, then is excellent and . Then we give a numerical criterion for the -very ampleness of excellent classes with , which in many cases is a necessary and sufficient condition.

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Additional Information

**Cindy De Volder**

Affiliation:
Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, S22, B-9000 Ghent, Belgium

Email:
cindy.devolder@ugent.be

**Halszka Tutaj-Gasinska**

Affiliation:
Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, PL-30348 Kraków, Poland – and – Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, PL-00956 Warszawa, Poland

Email:
htutaj@im.uj.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-09-10037-0

Keywords:
$k$-very ample,
anticanonical rational surface

Received by editor(s):
May 17, 2008

Received by editor(s) in revised form:
January 24, 2009, and April 30, 2009

Published electronically:
July 10, 2009

Communicated by:
Ted Chinburg

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.