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An Abel map to the
compactified Picard scheme realizes Poincaré duality
Jesse Leo Kass and Kirsten Wickelgren |
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Algebraic & Geometric Topology 15 (2015) 319–369
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Abstract |
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For a smooth algebraic curve over a field, applying to the Abel map to the Picard scheme of modulo its boundary realizes the Poincaré duality isomorphism We show the analogous statement for the Abel map to the compactified Picard, or Jacobian, scheme, namely this map realizes the Poincaré duality isomorphism . In particular, of this Abel map is an isomorphism. In proving this result, we prove some results about that are of independent interest. The singular curve has a unique singularity that is an ordinary fold point, and we describe the compactified Picard scheme of such a curve up to universal homeomorphism using a presentation scheme. We construct a Mayer–Vietoris sequence for certain pushouts of schemes, and an isomorphism of functors |
Keywords
Abel map, compactified Picard scheme, compactified
Jacobian, Poincaré duality
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Mathematical Subject Classification 2010
Primary: 14F35
Secondary: 14D20, 14F20
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References |
Publication
Received: 15 January 2014
Revised: 24 June 2014
Accepted: 9 July 2014
Published: 23 March 2015
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Authors |
| Jesse Leo Kass | |
| Department of Mathematics University of South Carolina 1523 Greene Street Columbia, SC 29208 USA |
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| http://www2.iag.uni-hannover.de/~kass/ | |
| Kirsten Wickelgren | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332 USA |
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| http://people.math.gatech.edu/~kwickelgren3/ | |
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