A Néron model of the universal jacobian
 
 
Description: 

Every non-singular algebraic curve C has a jacobian J, which is an abelian variety. Choosing a point on the curve determines an `abel-jacobi' map from C to J. The same constructions can be made in families: given a family of non-singular curves (together with a section), one obtains a family of abelian varieties, and an abel-jacobi map. We are interested in what happens when such a family of non-singular pointed curves degenerates to a singular pointed curve. In the case where the base-space of the family has dimension 1 (a `1-parameter family'), this is completely understood due to work of André Néron in the 1960s. However, when the base space has higher dimension things become more difficult. We describe a seemingly-new combinatorial invariant which controls these degenerations. In the case of the jacobian of the universal stable curve, we will use this to construct a `minimal' base-change after which a Néron model exists.

Date:  2015-04-13
Start Time:   14:30
Speaker:  David Holmes (Univ. Leiden, The Netherlands)
Institution:  University of Leiden (The Netherlands)
Place:  Room 5.5 DMUC
Research Groups: -Algebra and Combinatorics
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