Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Obstructions to deforming curves on a $ 3$-fold, I: A generalization of Mumford's example and an application to $ \operatorname{Hom}$ schemes


Authors: Shigeru Mukai and Hirokazu Nasu
Journal: J. Algebraic Geom. 18 (2009), 691-709
DOI: https://doi.org/10.1090/S1056-3911-08-00502-X
Published electronically: August 14, 2008
MathSciNet review: 2524595
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Abstract | References | Additional Information

Abstract: We give a sufficient condition for a first order infinitesimal deformation of a curve on a $ 3$-fold to be obstructed. As application we construct generically non-reduced components of the Hilbert schemes of uniruled $ 3$-folds and the Hom scheme from a general curve of genus five to a general cubic $ 3$-fold.


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Additional Information

Shigeru Mukai
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: mukai@kurims.kyoto-u.ac.jp

Hirokazu Nasu
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
Email: nasu@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S1056-3911-08-00502-X
Received by editor(s): May 23, 2007
Received by editor(s) in revised form: September 28, 2007
Published electronically: August 14, 2008
Additional Notes: During this research, the first author was supported in part by the JSPS Grant-in-Aid for Scientific Research (B) 17340006. The second author was supported in part by the 21st century COE program “Formation of an International Center of Excellence in the Frontier of Mathematics and Fostering of Researchers in Future Generations”.

American Mathematical Society