Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Bicanonical pencil of a determinantal Barlow surface
HTML articles powered by AMS MathViewer

by Yongnam Lee
Trans. Amer. Math. Soc. 353 (2001), 893-905
DOI: https://doi.org/10.1090/S0002-9947-00-02609-X
Published electronically: November 8, 2000
PDF | Request permission

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.
References
  • Enrico Arbarello and Maurizio Cornalba, The Picard groups of the moduli spaces of curves, Topology 26 (1987), no. 2, 153–171. MR 895568, DOI 10.1016/0040-9383(87)90056-5
  • Rebecca Barlow, A simply connected surface of general type with $p_g=0$, Invent. Math. 79 (1985), no. 2, 293–301. MR 778128, DOI 10.1007/BF01388974
  • Arnaud Beauville, Variétés de Prym et jacobiennes intermédiaires, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 3, 309–391 (French). MR 472843, DOI 10.24033/asens.1329
  • Arnaud Beauville, L’application canonique pour les surfaces de type général, Invent. Math. 55 (1979), no. 2, 121–140 (French). MR 553705, DOI 10.1007/BF01390086
  • O. Debarre, Inégalités numériques pour les surfaces de type général, Bull. Soc. Math. France 110 (1982), no. 3, 319–346 (French, with English summary). With an appendix by A. Beauville. MR 688038
  • F. Catanese, Babbage’s conjecture, contact of surfaces, symmetric determinantal varieties and applications, Invent. Math. 63 (1981), no. 3, 433–465. MR 620679, DOI 10.1007/BF01389064
  • F. Catanese, Pluricanonical mapping of surfaces with $K^{2}=1,2$, $q=p_{g}=0$, C.I.M.E. 1977 Algebraic Surfaces, Liguori, Napoli (1981), 249–266.
  • Fabrizio Catanese and Claude LeBrun, On the scalar curvature of Einstein manifolds, Math. Res. Lett. 4 (1997), no. 6, 843–854. MR 1492124, DOI 10.4310/MRL.1997.v4.n6.a5
  • F. Catanese and R. Pignatelli, On simply connected Godeaux surfaces, Preprint (1999).
  • Takao Fujita, On Kähler fiber spaces over curves, J. Math. Soc. Japan 30 (1978), no. 4, 779–794. MR 513085, DOI 10.2969/jmsj/03040779
  • Joe Harris and David Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), no. 1, 23–88. With an appendix by William Fulton. MR 664324, DOI 10.1007/BF01393371
  • János Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 32, Springer-Verlag, Berlin, 1996. MR 1440180, DOI 10.1007/978-3-662-03276-3
  • Y. Lee, Degeneration of numerical Godeaux surfaces, Ph.D. Thesis, University of Utah (1997).
  • Y. Lee, A compactification of a family of determinantal Godeaux surfaces, Trans. Amer. Math. Soc. 352 (2000), 5013–5023.
  • Yoichi Miyaoka, Tricanonical maps of numerical Godeaux surfaces, Invent. Math. 34 (1976), no. 2, 99–111. MR 409481, DOI 10.1007/BF01425477
  • Miles Reid, Surfaces with $p_{g}=0$, $K^{2}=1$, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 25 (1978), no. 1, 75–92. MR 494596
  • M. Texidor, The divisor of curves with a vanishing theta-null, Compositio Math. 66 (1988), 15–22.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14J10, 14J29
  • Retrieve articles in all journals with MSC (2000): 14J10, 14J29
Bibliographic 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
  • 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.
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 893-905
  • MSC (2000): Primary 14J10, 14J29
  • DOI: https://doi.org/10.1090/S0002-9947-00-02609-X
  • MathSciNet review: 1707700