Geometry of theta divisors --- a survey

Details Geometry of theta divisors --- a survey Geometry of theta divisors --- a survey

2012-04-12

arxiv.org/abs/1204.2734v1

Mathematics

Algebraic Geometry

Scientific paper

We survey the geometry of the theta divisor and discuss various loci of principally polarized abelian varieties (ppav) defined by imposing conditions on its singularities. The loci defined in this way include the (generalized) Andreotti-Mayer loci, but also other geometrically interesting cycles such as the locus of intermediate Jacobians of cubic threefolds. We shall discuss questions concerning the dimension of these cycles as well as the computation of their class in the Chow or the cohomology ring. In addition we consider the class of their closure in suitable toroidal compactifications and describe degeneration techniques which have proven useful. For this we include a discussion of the construction of the universal family of ppav with a level structure and its possible extensions to toroidal compactifications. The paper contains numerous open questions and conjectures.

Affiliated with

Also associated with

No associations

Rating

Geometry of theta divisors --- a survey does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometry of theta divisors --- a survey, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry of theta divisors --- a survey will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-312525