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Bicanonical pencil of a determinantal Barlow surface


Author: Yongnam Lee
Journal: Trans. Amer. Math. Soc. 353 (2001), 893-905
MSC (2000): Primary 14J10, 14J29
Published electronically: November 8, 2000
MathSciNet review: 1707700
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Abstract:

In this paper, we study the bicanonical pencil of a Godeaux surface and of a determinantal Barlow surface. This study gives a simple proof for the unobstructedness of deformations of a determinantal Barlow surface. Then we compute the number of hyperelliptic curves in the bicanonical pencil of a determinantal Barlow surface via classical Prym theory.


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Additional Information

Yongnam Lee
Affiliation: Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-012, Korea
Address at time of publication: Department of Mathematics, Sogang University, Sinsu-dong, Mapo-gu, Seoul 121-742, Korea
Email: ynlee@ccs.sogang.ac.kr

DOI: https://doi.org/10.1090/S0002-9947-00-02609-X
Received by editor(s): October 15, 1997
Received by editor(s) in revised form: June 3, 1999
Published electronically: November 8, 2000
Additional Notes: The author would like to express his appreciation to professor Herb Clemens for valuable suggestions that made this work possible. Also the author would like to thank Professor Fabrizio Catanese for the use of his approach and the results in his recent preprint (written with Pignatelli) to solve the problem of hyperelliptic curves. Finally, the author would like to thank the referee for many interesting suggestions and corrections. Most of this work is the part of a Ph.D. thesis submitted to the University of Utah in 1997, and is partially supported by the Korea Institute for Advanced Study.
Article copyright: © Copyright 2000 American Mathematical Society