Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Geometry of the Space of Holomorphic Maps from a Riemann Surface
  into Complex Projective Space   In this paper we study the topology of the spaces Hol(M,P{n},k) of (basepoint
preserving) holomorphic maps of a given degree k from a Riemann surface M of
genus g>0 into the n-th complex projective space P{n}, n>0. Using symmetric
products of the surface as well as the geometry of the associated Abel-Jacobi
maps, we construct an explicit topological compactification of Hol(M,P{n},k)
which allow us to construct spectral sequences with known E_1-terms that can be
used to determine the homology groups of Hol(M,P{n},k). Complete calculations
are given for the elliptic case (g=1). Complete rational calculations are also
given for hyperelliptic curves.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph