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Trigonal deformations of rank one and Jacobians | | Valentina Beorchia
; Gian Pietro Pirola
; Francesco Zucconi
; | | Date: |
21 Dec 2018 | | Abstract: | In this paper we study the infinitesimal deformations of a trigonal curve
that preserve the trigonal series and such that the associate infinitesimal
variation of Hodge structure (IVHS) is of rank 1. We show that if the genus g
is greater or equal to 8 or g=6,7 and the curve is Maroni general, this locus
is zero dimensional. Moreover, we complete a result of Naranjo and Pirola. We
show in fact that if the genus g is greater or equal to 6, the hyperelliptic
locus is the only 2g-1-dimensional sub-locus Y of the moduli space of curves of
genus g, such that for the general element [C] in Y, its Jacobian J(C) is
dominated by a hyperelliptic Jacobian of genus g’ greater or equal to g. | | Source: | arXiv, 1812.9248 | | Services: | Forum | Review | PDF | Favorites | |
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