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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Deformation of quintic threefolds to the chordal variety


Author: Adrian Zahariuc
Journal: Trans. Amer. Math. Soc. 370 (2018), 6493-6513
MSC (2010): Primary 14H45; Secondary 05C50, 14N10, 14J32, 14D06
DOI: https://doi.org/10.1090/tran/7154
Published electronically: February 8, 2018
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Abstract: We consider a family of quintic threefolds specializing to a certain reducible threefold. We describe the space of genus zero stable morphisms to the central fiber, as defined by J. Li. As an application of a straightforward extension, we prove the existence of rigid stable maps with smooth source of arbitrary genus and sufficiently high degree to very general quintics.


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Additional Information

Adrian Zahariuc
Affiliation: Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
Address at time of publication: Department of Mathematics, University of California Davis, One Shields Avenue, Davis, California 95616
Email: azahariuc@math.ucdavis.edu

DOI: https://doi.org/10.1090/tran/7154
Keywords: Quintic threefold, degeneration, rigid embedded curve, rigid stable map, chordal variety, graph eigenvalue
Received by editor(s): July 22, 2016
Received by editor(s) in revised form: December 14, 2016
Published electronically: February 8, 2018
Additional Notes: This work was partially supported by National Science Foundation grant DMS-1308244 Nonlinear Analysis on Sympletic, Complex Manifolds, General Relativity, and Graphs.
Article copyright: © Copyright 2018 American Mathematical Society

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