Duke Mathematical Journal

Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants

Jean-Yves Welschinger

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Abstract

Let X be a real algebraic convex 3-manifold whose real part is equipped with a Pin structure. We show that every irreducible real rational curve with nonempty real part has a canonical spinor state belonging to {± 1}. The main result is then that the algebraic count of the number of real irreducible rational curves in a given numerical equivalence class passing through the appropriate number of points does not depend on the choice of the real configuration of points, provided that these curves are counted with respect to their spinor states. These invariants provide lower bounds for the total number of such real rational curves independently of the choice of the real configuration of points.

Article information

Source
Duke Math. J., Volume 127, Number 1 (2005), 89-121.

Dates
First available in Project Euclid: 4 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1109963911

Digital Object Identifier
doi:10.1215/S0012-7094-04-12713-7

Mathematical Reviews number (MathSciNet)
MR2126497

Zentralblatt MATH identifier
1084.14056

Subjects
Primary: 14N35, 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
Secondary: 14P25: Topology of real algebraic varieties

Citation

Welschinger, Jean-Yves. Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants. Duke Math. J. 127 (2005), no. 1, 89--121. doi:10.1215/S0012-7094-04-12713-7. https://projecteuclid.org/euclid.dmj/1109963911


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