Volume 9, issue 2 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Counting rational curves of arbitrary shape in projective spaces

Aleksey Zinger

Geometry & Topology 9 (2005) 571–697

arXiv: math.AG/0210146

Abstract

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.

Keywords
enumerative geometry, projective spaces, rational curves
Mathematical Subject Classification 2000
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
Authors
Aleksey Zinger
Department of Mathematics
Stanford University
Stanford
California 94305-2125
USA
http://math.stanford.edu/~azinger/