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Explicit computations on the desingularized Kummer surface
Authors:
V. G. Lopez Neumann and Constantin Manoil
Journal:
Math. Comp. 81 (2012), 1149-1161
MSC (2010):
Primary 14J28, 14M15; Secondary 14J50
Posted:
September 30, 2011
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Additional Information
Abstract: We find formulas for the birational maps from a Kummer surface and its dual to their common minimal desingularization . We show how the nodes of and blow up. Then we give a description of the group of linear automorphisms of .
References
- 1.
Arnaud
Beauville, Surfaces algébriques complexes,
Société Mathématique de France, Paris, 1978 (French).
Avec une sommaire en anglais; Astérisque, No. 54. MR 0485887
(58 #5686)
- 2.
Patrick
Corn, Tate-Shafarevich groups and 𝐾3
surfaces, Math. Comp. 79
(2010), no. 269, 563–581. MR 2552241
(2011d:11139), http://dx.doi.org/10.1090/S0025-5718-09-02264-9
- 3.
J.
W. S. Cassels and E.
V. Flynn, Prolegomena to a middlebrow arithmetic of curves of genus
2, London Mathematical Society Lecture Note Series, vol. 230,
Cambridge University Press, Cambridge, 1996. MR 1406090
(97i:11071)
- 4.
Eugene
Victor Flynn, The Jacobian and formal group of a curve of genus 2
over an arbitrary ground field, Math. Proc. Cambridge Philos. Soc.
107 (1990), no. 3, 425–441. MR 1041476
(91b:14025), http://dx.doi.org/10.1017/S0305004100068729
- 5.
Phillip
Griffiths and Joseph
Harris, Principles of algebraic geometry, Wiley-Interscience
[John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR 507725
(80b:14001)
- 6.
R.
W. H. T. Hudson, Kummer’s quartic surface, Cambridge
Mathematical Library, Cambridge University Press, Cambridge, 1990. With a
foreword by W. Barth; Revised reprint of the 1905 original. MR 1097176
(92e:14033)
- 7.
Adam
Logan and Ronald
van Luijk, Nontrivial elements of Sha explained
through 𝐾3 surfaces, Math. Comp.
78 (2009), no. 265, 441–483. MR 2448716
(2010a:14048), http://dx.doi.org/10.1090/S0025-5718-08-02105-4
- 8.
V.G. Lopez-Neumann and C. Manoil, Explicit computations on the desingularized Kummer surface, arXiv:0906.0790v1.
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Additional Information
V. G. Lopez Neumann
Affiliation:
Faculdade de Matemática, Universidade Federal de Uberlândia, MG, Brazil
Email:
gonzalo@famat.ufu.br
Constantin Manoil
Affiliation:
Section de Mathématiques, Université de Genève, CP 64, 1211 Geneva 4, Switzerland
Address at time of publication:
Collège Sismondi, 3 Chemin Rigot, 1202 Genève (Geneva), Switzerland
Email:
constantin.manoil@edu.ge.ch
DOI:
http://dx.doi.org/10.1090/S0025-5718-2011-02547-0
PII:
S 0025-5718(2011)02547-0
Keywords:
Genus $2$ curves,
Kummer surfaces,
line complexes.
Received by editor(s):
July 3, 2009
Posted:
September 30, 2011
Article copyright:
© Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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