Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concomitants of Ternary Quartics and Vector-valued Siegel and
  Teichm\"uller Modular Forms of Genus Three   We show how one can use the representation theory of ternary quartics to
construct all vector-valued Siegel modular forms and Teichm\"uller modular
forms of degree 3. The relation between the order of vanishing of a concomitant
on the locus of double conics and the order of vanishing of the corresponding
modular form on the hyperelliptic locus plays an important role. We also
determine the connection between Teichm\"uller cusp forms on \overline{M}_g and
the middle cohomology of symplectic local systems on M_g. In genus 3, we make
this explicit in a large number of cases.

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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom