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Proefschrift

A monodromy criterion for existence of Neron models and a result on semi-factoriality

In the first part, we introduce a new condition, called toric-additivity, on a family of abelian varieties degenerating to a semi-abelian scheme over a normal crossing divisor.

Auteur
Orecchia, G.
Datum
27 april 2018
Links
Thesis in Leiden Repository

In the first part, we introduce a new condition, called toric-additivity, on a family of abelian varieties degenerating to a semi-abelian scheme over a normal crossing divisor. The condition depends only on the l-adic Tate module of the generic fibre, for a prime l invertible on S. We show that toric-additivity is strictly related to the property of existence of Neron models. In the second part, we consider the case of a family of nodal curves over a discrete valuation ring, having split singularities. We say that such a family is semi-factorial if every line bundle on the generic bre extends to a line bundle on the total space. We give a necessary and sufficient condition for semifactoriality, in terms of combinatorics of the dual graph of the special fibre.

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