Osservazioni sullo spazio dei moduli delle curve trigonali

Fabio Bardelli; Andrea Del Centina

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1981)

  • Volume: 70, Issue: 2, page 96-100
  • ISSN: 0392-7881

Abstract

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Let C be an algebraic projective smooth and trigonal curve of genus g ≥ 5 . In this paper we define, in a way equivalent to that followed by A. Maroni in [1], an integer m , called the species of C , which is a birational invariant having the property that 0 ≤ m ≤ g + 2 3 and m ⁢ — ⁢ g ≡ 0 mod(2). In section 1 we prove that for every g ( ≥ 5 ) and every m , as before, there are trigonal curves of genus g and species m . In section 2 we define the space ℳ g , 3 ; m 1 of moduli of trigonal curves of genus g and species m . We note that ℳ g , 3 ; m 1 is irreducible and unirational and we prove that d ⁢ i ⁢ m ⁢ ℳ g , 3 ; m 1 = 2 ⁢ g + 2 ⁢ — ⁢ m if m ≠ 0 and d ⁢ i ⁢ m ⁢ ℳ g , 3 ; 0 1 = 2 ⁢ g + 1 . As Corollaries we obtain the following facts: the general trigonal curve of even genus is of species 0 , the general trigonal curve of odd genus is of species 1 and the space ℳ g , 3 1 of moduli of trigonal curves of genus g is unirational. The results of this note are valid over any algebraically closed field of any characteristic.

How to cite

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Bardelli, Fabio, and Del Centina, Andrea. "Osservazioni sullo spazio dei moduli delle curve trigonali." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 70.2 (1981): 96-100. <http://eudml.org/doc/288713>.

@article{Bardelli1981,
author = {Bardelli, Fabio, Del Centina, Andrea},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {2},
number = {2},
pages = {96-100},
publisher = {Accademia Nazionale dei Lincei},
title = {Osservazioni sullo spazio dei moduli delle curve trigonali},
url = {http://eudml.org/doc/288713},
volume = {70},
year = {1981},
}

TY - JOUR
AU - Bardelli, Fabio
AU - Del Centina, Andrea
TI - Osservazioni sullo spazio dei moduli delle curve trigonali
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1981/2//
PB - Accademia Nazionale dei Lincei
VL - 70
IS - 2
SP - 96
EP - 100
LA - ita
UR - http://eudml.org/doc/288713
ER -

References

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  1. Maroni, A. (1946) - Serie lineari speciali sulle curve trigonali, «Ann. di Mat. Pura e Appl.», 25 IV. Zbl0061.35407
  2. Arbarello, E. e Cornalba, M.. Footnotes to a paper of Beniamino Segre, preprint. 
  3. Severi, F. (1922) - Sul teorema di esistenza di Riemann, «Rend, del Circolo Mat. di Palermo», XLVI. 
  4. Saint-Donat, B. (1973) - On Petri's analysis of the linear sistem of quadrics through a canonical curve, «Math. Ann.», 206. 
  5. Griffiths, P. e Harris, J. (1978) - Principles of algebraic geometry, Wiley. Zbl0408.14001
  6. Fulton, W. (1969) - Hurwitz schemes and irreducibility of the moduli of algebraic curves, «Ann. of Math.»90. Zbl0194.21901
  7. Mumford, D. (1965) - Geometric invariant theory, Springer-Verlag. 
  8. Turrini, C. (1979) - Gli automorfismi delle rigate geometriche razionali, «Ist. Lombardo Rend. Sc.» A, 113. Zbl0464.14014
  9. Hartshorne, R. (1977) - Algebraic geometry, Springer-Verlag. Zbl0367.14001

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