Counting rational curves of arbitrary shape in projective spaces

Details Counting rational curves of arbitrary shape in projective spaces Counting rational curves of arbitrary shape in projective spaces

2002-10-09

arxiv.org/abs/math/0210146v3

Geom. Topol. 9(2005) 571-697

Mathematics

Algebraic Geometry

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper16.abs.html

Scientific paper

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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