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You searched for subject:(Neron models). Showing records 1 – 2 of 2 total matches.

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Leiden University

1. Orecchia, G. A monodromy criterion for existence of Neron models and a result on semi-factoriality.

Degree: 2018, Leiden University

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. Advisors/Committee Members: Supervisor: Edixhoven S.J., Liu Q. Co-Supervisor: Holmes D..

Subjects/Keywords: Neron models; Jacobians; Degenerations; Line bundles; Neron models; Jacobians; Degenerations; Line bundles

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Orecchia, G. (2018). A monodromy criterion for existence of Neron models and a result on semi-factoriality. (Doctoral Dissertation). Leiden University. Retrieved from http://hdl.handle.net/1887/61150

Chicago Manual of Style (16th Edition):

Orecchia, G. “A monodromy criterion for existence of Neron models and a result on semi-factoriality.” 2018. Doctoral Dissertation, Leiden University. Accessed August 05, 2020. http://hdl.handle.net/1887/61150.

MLA Handbook (7th Edition):

Orecchia, G. “A monodromy criterion for existence of Neron models and a result on semi-factoriality.” 2018. Web. 05 Aug 2020.

Vancouver:

Orecchia G. A monodromy criterion for existence of Neron models and a result on semi-factoriality. [Internet] [Doctoral dissertation]. Leiden University; 2018. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/1887/61150.

Council of Science Editors:

Orecchia G. A monodromy criterion for existence of Neron models and a result on semi-factoriality. [Doctoral Dissertation]. Leiden University; 2018. Available from: http://hdl.handle.net/1887/61150


Leiden University

2. Akeyr, G. Dual complexes of semistable varieties.

Degree: 2019, Leiden University

This thesis is comprised of three chapters covering the theme of studying semistable varieties by looking at their dual combinatorial objects.The first chapter defines what it is to be a semistable variety. This is done in such a way as to generalize the case of semistable curves. The dual graph of such a variety has vertices corresponding to the the irreducible components of the variety, with edges between the vertices corresponding to connected components of the non-smooth loci. We show that this definition allows us to reproduce results as in the 1-dimensional case, where a condition on the dual graph called "alignment" is necessary for the existence of a Neron model of the Picard space of the variety.The second chapter is inspired by tropical geometry and seeks to define a good generalization of the tropical curve associated to a logarithmic curve over a logarithmic base scheme.The last chapter shows how, in the case of a semistable curve, the Artin fan associated to the curve has its underlying topological space naturally isomorphic to that of the dual graph. We prove additional results related to the existence of an associated logarithmic morphism. Advisors/Committee Members: Supervisor: Edixhoven B. Co-Supervisor: Holmes D..

Subjects/Keywords: Neron models; dual graphs; cone complexes; logarithmic geometry; tropical geometry; semistable morphisms; deformation theory; alignment; Picard spaces; Neron models; dual graphs; cone complexes; logarithmic geometry; tropical geometry; semistable morphisms; deformation theory; alignment; Picard spaces

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Akeyr, G. (2019). Dual complexes of semistable varieties. (Doctoral Dissertation). Leiden University. Retrieved from http://hdl.handle.net/1887/82073

Chicago Manual of Style (16th Edition):

Akeyr, G. “Dual complexes of semistable varieties.” 2019. Doctoral Dissertation, Leiden University. Accessed August 05, 2020. http://hdl.handle.net/1887/82073.

MLA Handbook (7th Edition):

Akeyr, G. “Dual complexes of semistable varieties.” 2019. Web. 05 Aug 2020.

Vancouver:

Akeyr G. Dual complexes of semistable varieties. [Internet] [Doctoral dissertation]. Leiden University; 2019. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/1887/82073.

Council of Science Editors:

Akeyr G. Dual complexes of semistable varieties. [Doctoral Dissertation]. Leiden University; 2019. Available from: http://hdl.handle.net/1887/82073

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