Gonality for stable curves and their maps with a smooth curve as their target

Edoardo Ballico

Open Mathematics (2009)

  • Volume: 7, Issue: 1, page 54-58
  • ISSN: 2391-5455

Abstract

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Here we study the deformation theory of some maps f: X → ℙr , r = 1, 2, where X is a nodal curve and f|T is not constant for every irreducible component T of X. For r = 1 we show that the “stratification by gonality” for any subset of [...] with fixed topological type behaves like the stratification by gonality of M g.

How to cite

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Edoardo Ballico. "Gonality for stable curves and their maps with a smooth curve as their target." Open Mathematics 7.1 (2009): 54-58. <http://eudml.org/doc/269390>.

@article{EdoardoBallico2009,
abstract = {Here we study the deformation theory of some maps f: X → ℙr , r = 1, 2, where X is a nodal curve and f|T is not constant for every irreducible component T of X. For r = 1 we show that the “stratification by gonality” for any subset of [...] with fixed topological type behaves like the stratification by gonality of M g.},
author = {Edoardo Ballico},
journal = {Open Mathematics},
keywords = {Stable curve; Brill-Noether theory; Plane nodal curve; Gonality; stable curve; plane nodal curve; gonality},
language = {eng},
number = {1},
pages = {54-58},
title = {Gonality for stable curves and their maps with a smooth curve as their target},
url = {http://eudml.org/doc/269390},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Edoardo Ballico
TI - Gonality for stable curves and their maps with a smooth curve as their target
JO - Open Mathematics
PY - 2009
VL - 7
IS - 1
SP - 54
EP - 58
AB - Here we study the deformation theory of some maps f: X → ℙr , r = 1, 2, where X is a nodal curve and f|T is not constant for every irreducible component T of X. For r = 1 we show that the “stratification by gonality” for any subset of [...] with fixed topological type behaves like the stratification by gonality of M g.
LA - eng
KW - Stable curve; Brill-Noether theory; Plane nodal curve; Gonality; stable curve; plane nodal curve; gonality
UR - http://eudml.org/doc/269390
ER -

References

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  2. [2] Buchweitz R.-O., Greuel G.-M., The Milnor number and deformations of complex curve singularities, Invent. Math., 1980, 58, 241–281 http://dx.doi.org/10.1007/BF01390254[Crossref] Zbl0458.32014
  3. [3] Caporaso L., A compactification of the universal Picard variety over the moduli space of stable curves, J. Amer. Math. Soc., 1994, 7, 589–660 http://dx.doi.org/10.2307/2152786[Crossref] Zbl0827.14014
  4. [4] Caporaso L., Brill-Noether theory of binary curves, preprint available at arXiv:math/0807.1484 
  5. [5] Ciliberto C., Harris J., Miranda R., On the surjectivity of the Wahl map, Duke Math. J., 1988, 57, 829–858 http://dx.doi.org/10.1215/S0012-7094-88-05737-7[Crossref] Zbl0684.14009
  6. [6] Harris J., Mumford D., On the Kodaira dimension of the moduli space of curves, Invent. Math., 1982, 67, 23–86 http://dx.doi.org/10.1007/BF01393371[Crossref] Zbl0506.14016
  7. [7] Sernesi E., Deformations of algebraic schemes, Springer, Berlin, 2006 Zbl1102.14001
  8. [8] Seshadri C., Fibrés vectoriels sur les courbes algébriques, Astérisque 96, Société Mathématique de France, Paris, 1982 Zbl0517.14008
  9. [9] Tannenbaum A., Families of algebraic curves with nodes, Compositio Math., 1980, 41, 107–119 Zbl0399.14018

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