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

top
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

top

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

top
  1. [1] Bayer D., Eisenbud D., Graph curves, Adv. Math., 1991, 86, 1–40 http://dx.doi.org/10.1016/0001-8708(91)90034-5[Crossref] 
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.