Geometry & Topology, Vol. 9 (2005) Paper no. 16, pages 571--697.

Counting rational curves of arbitrary shape in projective spaces

Aleksey Zinger

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

AMS subject classification. Primary: 14N99, 53D99. Secondary: 55R99.

DOI: 10.2140/gt.2005.9.571

E-print: arXiv:math.AG/0210146

Submitted to GT on 2 August 2003. (Revised 26 February 2005.) Paper accepted 29 March 2005. Paper published 19 April 2005.

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Aleksey Zinger
Department of Mathematics, Stanford University
Stanford, CA 94305-2125, USA

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