Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of theta divisors --- a survey   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.

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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph