IJPAM: Volume 88, No. 3 (2013)

CURVES WITH SEVERAL THETA-CHARACTERISTICS
WITH A PRESCRIBED NUMBER OF SECTIONS: A QUESTION LIST

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. Let ${^{[s]}}\mathcal {S}_g$, $s>0$, $g\ge 2$, be the moduli scheme of all $(C,L_1,\dots ,L_s)$, where $C$ is a smooth curve of genus $g$ and each $L_i$ is a theta-characteristic. For all $r_i>0$, $1\le i \le s$, set $^{[s]}\mathcal {S}^{r_1,\dots ,r_s}_g:= \{(C,L_1,\dots ,L_s)\in {^{[s]}}\mathcal {S}_g: h^0(L_i) =r_i+1$ for all $i\}$. Here we raise several questions on these algebraic sets. We show that if $T$ is a general element of a component of $^{[s]}\mathcal {S}^{r_1,\dots ,r_s}_g$ with the expect codimension $\sum _{i=1}^{s} \binom{r_i+1}{2}$ and $(C,L_1,\dots ,L_s)$ is general in $T$, then each $L_i$ has no base points.

Received: June 11, 2013

AMS Subject Classification: 14H10, 14H51

Key Words and Phrases: theta-characteristic, spin curve, Gaussian map

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DOI: 10.12732/ijpam.v88i3.5 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 3