By studying the innitesimal variations of the Hodge structure and a generalization of the classical Babbage{Enriques{Petri theorem, we prove that the Jacobian variety of a generic element of a codimension k subvariety of Mg is not isogenous to dierent Jacobian if g > 3k + 4. We extend this result to k = 1, g > 5 by using degeneration methods. 1
Isogenies of Jacobians
PIROLA, GIAN PIETRO
2016-01-01
Abstract
By studying the innitesimal variations of the Hodge structure and a generalization of the classical Babbage{Enriques{Petri theorem, we prove that the Jacobian variety of a generic element of a codimension k subvariety of Mg is not isogenous to dierent Jacobian if g > 3k + 4. We extend this result to k = 1, g > 5 by using degeneration methods. 1File in questo prodotto:
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