Volume 8 (2006)

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On the rigidity of stable maps to Calabi–Yau threefolds

Jim Bryan and Rahul Pandharipande

Geometry & Topology Monographs 8 (2006) 97–104

DOI: 10.2140/gtm.2006.8.97

arXiv: math.AG/0405204

Abstract

If X⊂Y is a nonsingular curve in a Calabi–Yau threefold whose normal bundle NX/Y is a generic semistable bundle, are the local Gromov–Witten invariants of X well defined? For X of genus two or higher, the issues are subtle. We will formulate a precise line of inquiry and present some results, some positive and some negative.

Keywords

Calabi–Yau manifold, deformations, Gromov–Witten theory

Mathematical Subject Classification

Primary: 14J32

Secondary: 14N35

References
Publication

Received: 19 April 2004
Revised: 2 February 2005
Accepted: 11 March 2005
Published: 22 April 2006

Authors
Jim Bryan
Department of Mathematics
University of British Columbia
Vancouver
BC
Canada
http://www.math.ubc.ca/~jbryan/
Rahul Pandharipande
Department of Mathematics
Princeton University
Princeton
NJ
USA