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Kummer surfaces and the computation of the Picard group

Title data

Elsenhans, Andreas-Stephan ; Jahnel, Jörg:
Kummer surfaces and the computation of the Picard group.
In: LMS Journal of Computation and Mathematics. Vol. 15 (2012) . - pp. 84-100.
ISSN 1461-1570
DOI: https://doi.org/10.1112/S1461157012000022

Project information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We test R. van Luijk’s method for computing the Picard group of a K3 surface. The examples considered are the resolutions of Kummer quartics in P^3. Using the theory of abelian varieties, the Picard group may be computed directly in this case. Our experiments show that the upper bounds provided by van Luijk’s method are sharp when sufficiently many primes are used. In fact, there are a lot of primes that yield a value close to the exact one. However, for many but not all Kummer surfaces V of Picard rank 18, we have rk Pic(V_(bar(F)_p)) >= 20 for a set of primes of density at least 1/2.

Further data

Item Type: Article in a journal
Refereed: Yes
Subject classification: 2010 Mathematics Subject Classification Code: 14J28 (14F20 14K99 14C22)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 08 Apr 2016 08:40
Last Modified: 08 Apr 2016 08:40
URI: https://eref.uni-bayreuth.de/id/eprint/32133