Theta loci and deformation theory

Claudio Fontanari

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2002)

  • Volume: 13, Issue: 2, page 135-142
  • ISSN: 1120-6330

Abstract

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We investigate deformation-theoretical properties of curves carrying a half-canonical linear series of fixed dimension. In particular, we improve the previously known bound on the dimension of the corresponding loci in the moduli space and we obtain a natural description of the tangent space to higher theta loci.

How to cite

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Fontanari, Claudio. "Theta loci and deformation theory." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.2 (2002): 135-142. <http://eudml.org/doc/252380>.

@article{Fontanari2002,
abstract = {We investigate deformation-theoretical properties of curves carrying a half-canonical linear series of fixed dimension. In particular, we improve the previously known bound on the dimension of the corresponding loci in the moduli space and we obtain a natural description of the tangent space to higher theta loci.},
author = {Fontanari, Claudio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Theta characteristics; Infinitesimal deformations; Moduli of curves; theta characteristics; infinitesimal deformations; moduli of curves},
language = {eng},
month = {6},
number = {2},
pages = {135-142},
publisher = {Accademia Nazionale dei Lincei},
title = {Theta loci and deformation theory},
url = {http://eudml.org/doc/252380},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Fontanari, Claudio
TI - Theta loci and deformation theory
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/6//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 2
SP - 135
EP - 142
AB - We investigate deformation-theoretical properties of curves carrying a half-canonical linear series of fixed dimension. In particular, we improve the previously known bound on the dimension of the corresponding loci in the moduli space and we obtain a natural description of the tangent space to higher theta loci.
LA - eng
KW - Theta characteristics; Infinitesimal deformations; Moduli of curves; theta characteristics; infinitesimal deformations; moduli of curves
UR - http://eudml.org/doc/252380
ER -

References

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  1. Arbarello, E. - Cornalba, M., Su una congettura di Petri. Comment. Math. Helvetici, 56, 1981, 1-38. Zbl0505.14002MR615613DOI10.1007/BF02566195
  2. Arbarello, E. - Cornalba, M., Footnotes to a paper of Beniamino Segre. Math. Ann., 256, 1981, 341-362. Zbl0454.14023MR626954DOI10.1007/BF01679702
  3. Arbarello, E. - Cornalba, M. - Griffiths, P. - Harris, J., Special divisors on algebraic curves. Informal lecture notes distributed in conjunction with the principal lectures at the Regional Algebraic Geometry Conference, Athens, Georgia, May 7 - May 12, 1979. 
  4. Arbarello, E. - Cornalba, M. - Griffiths, P. - Harris, J., Geometry of Algebraic Curves, I. Grundlehren Math. Wiss., vol. 267, Springer-Verlag, 1985. Zbl0559.14017MR770932
  5. Harris, J., Theta characteristics on algebraic curves. Trans. Amer. Math. Soc., 271, 1982, 611-638. Zbl0513.14025MR654853DOI10.2307/1998901
  6. Mumford, D., Theta characteristics of an algebraic curve. Ann. Ec. Norm. Sup., (4) 4 ,1971, 181-192. Zbl0216.05904MR292836
  7. Nagaraj, D.S., On the moduli of curves with theta-characteristics. Compositio Math., 75, 1990, 287-297. Zbl0726.14019MR1070415
  8. Segre, B., Sulle curve algebriche le cui tangenti appartengono al massimo numero di complessi lineari indipendenti. Atti Acc. Lincei Mem. fis., (6) 2, 1927, 578-592. JFM52.0682.02
  9. Teixidor i Bigas, M., Half-canonical series on algebraic curves. Trans. Amer. Math. Soc., 302, 1987, 99-115. Zbl0627.14022MR887499DOI10.2307/2000899

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