Geometry of families of nodal curves
on the blown-up projective plane
Authors:
Gert-Martin Greuel, Christoph Lossen and Eugenii Shustin
Journal:
Trans. Amer. Math. Soc. 350 (1998), 251-274
MSC (1991):
Primary 14H10
DOI:
https://doi.org/10.1090/S0002-9947-98-02055-8
MathSciNet review:
1443875
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be the projective plane blown up at
generic points. Denote by
the strict transform of a generic straight line on
and the exceptional divisors of the blown-up points on
respectively. We consider the variety
of all irreducible curves
in
with
nodes as the only singularities and give asymptotically nearly optimal sufficient conditions for its smoothness, irreducibility and non-emptiness. Moreover, we extend our conditions for the smoothness and the irreducibility to families of reducible curves. For
we give the complete answer concerning the existence of nodal curves in
.
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Additional Information
Gert-Martin Greuel
Affiliation:
Universität Kaiserslautern, Fachbereich Mathematik, Erwin-Schrödinger-Straße, D – 67663 Kaiserslautern, Germany
Email:
greuel@mathematik.uni-kl.de
Christoph Lossen
Affiliation:
Universität Kaiserslautern, Fachbereich Mathematik, Erwin-Schrödinger-Straße, D – 67663 Kaiserslautern, German
Email:
lossen@mathematik.uni-kl.de
Eugenii Shustin
Affiliation:
Tel Aviv University, School of Mathematical Sciences, Ramat Aviv, Tel Aviv 69978, Israel
Email:
shustin@math.tau.ac.il
DOI:
https://doi.org/10.1090/S0002-9947-98-02055-8
Keywords:
Nodal curves,
nodes,
families of curves,
blown--up projective space,
existence,
equisingular deformation
Received by editor(s):
February 1, 1996
Article copyright:
© Copyright 1998
American Mathematical Society