Geometry & Topology

Counting rational curves of arbitrary shape in projective spaces

Aleksey Zinger

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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.

Article information

Geom. Topol., Volume 9, Number 2 (2005), 571-697.

Received: 2 August 2003
Revised: 26 February 2005
Accepted: 29 March 2005
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 14N99: None of the above, but in this section 53D99: None of the above, but in this section
Secondary: 55R99: None of the above, but in this section

enumerative geometry projective spaces rational curves


Zinger, Aleksey. Counting rational curves of arbitrary shape in projective spaces. Geom. Topol. 9 (2005), no. 2, 571--697. doi:10.2140/gt.2005.9.571.

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