Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Period Mappings and Ampleness of the Hodge line bundle   We discuss progress towards a conjectural Hodge theoretic completion of a
period map. The completion is defined, and we conjecture that it admits the
structure of a compact complex analytic variety. The conjecture is proved when
the image of the period map has dimension 1,2. Assuming the conjecture holds,
we then prove that the augmented Hodge line bundle extends to an ample line
bundle on the completion. In particular, the completion is a projective
algebraic variety that compactifies the image, analogous to the
Satake-Baily-Borel compactification.

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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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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: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg