Geometry & Topology

Counting rational curves of arbitrary shape in projective spaces

Aleksey Zinger

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799602

Digital Object Identifier
doi:10.2140/gt.2005.9.571

Mathematical Reviews number (MathSciNet)
MR2140990

Zentralblatt MATH identifier
1086.14045

Subjects
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

Keywords
enumerative geometry projective spaces rational curves

Citation

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. https://projecteuclid.org/euclid.gt/1513799602


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