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A compactification of a family of determinantal Godeaux surfaces

Author: Yongnam Lee
Journal: Trans. Amer. Math. Soc. 352 (2000), 5013-5023
MSC (2000): Primary 14J10, 14J29
Published electronically: June 13, 2000
MathSciNet review: 1624186
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In this paper, we present a geometric description of the compactification of the family of determinantal Godeaux surfaces, via the study of the bicanonical pencil and using classical Prym theory. In particular, we reduce the problem of compactifying the space of bicanonical pencils of determinantal Godeaux surfaces to the compactification of the family of twisted cubic curves in $\mathbb{P}^{3}$ with certain given tangent conditions.

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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

Received by editor(s): November 30, 1997
Received by editor(s) in revised form: March 29, 1998
Published electronically: June 13, 2000
Additional Notes: The author would like to express his appreciation to Professor Herb Clemens for bringing his attention to this work, and for the valuable suggestions that made it possible. Also he would like to thank the referee for some comments. This work is part of a Ph.D. thesis submitted to the University of Utah in 1997. It was partially supported by the Korea Institute for Advanced Study
Article copyright: © Copyright 2000 American Mathematical Society

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