an:04019219
Zbl 0627.14022
Teixidor i Bigas, Montserrat
Half-canonical series on algebraic curves
EN
Trans. Am. Math. Soc. 302, 99-115 (1987).
00153113
1987
j
14H10 14C20 14D15
half-canonical series; linear system; moduli space of curves; deformation
Let \({\mathcal M}^ r_ g\) be the subloci of the moduli space \({\mathcal M}_ g\) of curves of genus \(g\) of those having a halfcanonical \(g^ s_{g- 1}\) with \(s\geq r\). The author gives the upper bound \(3g-3r+2\) for the dimension of \({\mathcal M}^ r_ g\) (which is sharp in the sense that for every r there is one g for which it is attained) and determines the codimension (in \({\mathcal M}_ g)\) in the case \(r\leq 4\). Also when \(r\leq 4\) the author proves that the generic point in every component of \({\mathcal M}^ r_ g\) has a unique halfcanonical \(g^ r_{g-1}.\)
The above results are obtained mainly by using deformation techniques developed by \textit{E. Arbarello} and \textit{M. Cornalba} [Comment. Math. Helv. 56, 1-38 (1981; Zbl 0505.14002) and Math. Ann. 256, 341-362 (1981; Zbl 0454.14023)].
A.Del Centina
Zbl 0461.14006; Zbl 0505.14002; Zbl 0454.14023