We study the infinitesimal deformations of a trigonal curve that preserve the trigonal series and such that the associate infinitesimal variation of Hodge structure is of rank 1. We show that if g ≥ 8 or g = 6,7 and the curve is Maroni general, this locus is zero dimensional. Moreover, we complete the result [10, Theorem 1.6]. We show in fact that if g ≥ 6, the hyperelliptic locus M1g,2 is the only 2g − 1-dimensional sub-locus Y of the moduli space Mg of curves of genus g, such that for the general element [C] ∈ Y, its Jacobian J(C) is dominated by a hyperelliptic Jacobian of genus g′ ≥ g.
Trigonal Deformations of Rank One and Jacobians
Gian Pietro Pirola;
2021-01-01
Abstract
We study the infinitesimal deformations of a trigonal curve that preserve the trigonal series and such that the associate infinitesimal variation of Hodge structure is of rank 1. We show that if g ≥ 8 or g = 6,7 and the curve is Maroni general, this locus is zero dimensional. Moreover, we complete the result [10, Theorem 1.6]. We show in fact that if g ≥ 6, the hyperelliptic locus M1g,2 is the only 2g − 1-dimensional sub-locus Y of the moduli space Mg of curves of genus g, such that for the general element [C] ∈ Y, its Jacobian J(C) is dominated by a hyperelliptic Jacobian of genus g′ ≥ g.File in questo prodotto:
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