scholarly journals Arithmetic of Split Kummer Surfaces: Montgomery Endomorphism of Edwards Products

2011 ◽  
pp. 238-245 ◽  
Author(s):  
David Kohel
Keyword(s):  
Kummer Surfaces

scholarly journals Kummer surfaces in characteristic $2$

1974 ◽  
Vol 50 (9) ◽  
pp. 718-722 ◽  
Author(s):  
Tetsuji Shioda
Keyword(s):  
Kummer Surfaces ◽  
Characteristic 2

scholarly journals Kummer surfaces and the computation of the Picard group

2012 ◽  
Vol 15 ◽  
pp. 84-100 ◽  
Author(s):  
Andreas-Stephan Elsenhans ◽  
Jörg Jahnel
Keyword(s):  
Abelian Varieties ◽  
Upper Bounds ◽  
Picard Group ◽  
A Value ◽  
Kummer Surfaces

AbstractWe 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 ℙ3. 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 ${\rm rk}\,{\rm Pic}(V_{\overline {\mathbb F}_{\hspace *{-.8pt}p}}) \geq 20$ for a set of primes of density at least 1/2.

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