Counting rational curves of arbitrary shape in projective spaces

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.

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

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• Enumeration of curves with two singular points
• Rational Cuspidal Curves in a moving family of ${\mathbb{P}}^2$
• Counting rational curves with an $m$-fold point
• Enumeration of Rational Cuspidal Curves via the WDVV equation