Algebra Seminar, Christelle Vincent (UVM): "Compuiting equations in hyperelliptic curves whose Jacobian has CM"

Friday, November 6, 2015
1:10 PM - 2:00 PM (ET)
Exley Science Center (Tower)
Event Type
Seminar/Colloquium
Contact
Caryn Canalia
Department
Mathematics and Computer Sciene
Link
https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=65636

Abstract:

It is known that given a totally imaginary sextic field with totally real cubic subfield (a so-called CM sextic field) there exists a non-empty finite set of abelian varieties of dimension 3 that have CM by this field. Under certain conditions on the field and the CM-type, this abelian variety can be guaranteed to be principally polarized and simple. 

In this talk, we begin by reviewing quickly the situation for elliptic curves with complex multiplication, which is the dimension 1 case of the work we present. We then move to the dimension 3 case, and present an algorithm that takes as input such a field and CM-type, and outputs a period matrix for such an abelian variety. We then check computationally if the abelian variety is the Jacobian of a hyperelliptic curve, and compute an equation for the curve if this is the case.

This is joint work with J. Balakrishnan, S. Ionica and K. Lauter.

Algebra Seminar, Christelle Vincent (UVM): "Compuiting equations in hyperelliptic curves whose Jacobian has CM" 1:10 PM - 2:00 PM (ET)
Exley Science Center (Tower)
265 Church Street, Middletown, CT 06457
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