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G&T Monographs |
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Counting rational curves of arbitrary shape in projective
spaces
Aleksey Zinger
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Geometry & Topology 9 (2005)
571–697
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Abstract
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We present an approach to a large class of enumerative problems concerning rational
curves in projective spaces. This approach uses analysis to obtain topological
information about moduli spaces of stable maps. We demonstrate it by enumerating
one-component rational curves with a triple point or a tacnodal point in
the three-dimensional projective space and with a cusp in any projective
space.
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Keywords
enumerative geometry, projective spaces,
rational curves
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Mathematical Subject Classification
Primary: 14N99, 53D99
Secondary: 55R99
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Publication
Received: 2 August 2003
Revised: 26 February 2005
Accepted: 29 March 2005
Published: 19 April 2005
Proposed: Frances Kirwan
Seconded: Ralph Cohen, Gang Tian
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