The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
نویسندگان
چکیده
منابع مشابه
The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
The purpose of this paper is a description of a model of Kummer surfaces in characteristic 2, together with the associated formulas for the pseudo-group law. Since the classical model has bad reduction, a renormalization of the parameters is required, that can be justified using the theory of algebraic theta functions. The formulas that are obtained are very efficient and may be useful in crypt...
متن کاملThe arithmetic of characteristic 2 Kummer surfaces
The purpose of this paper is a description of a model of Kummer surfaces in characteristic 2, together with the associated formulas for the pseudo-group law. Since the classical model has bad reduction, a renormalization of the parameters is required, that can be justified using the theory of algebraic theta functions. The formulas that are obtained are very efficient and may be useful in crypt...
متن کاملArithmetic of Split Kummer Surfaces: Montgomery Endomorphism of Edwards Products
Let E be an elliptic curve, K1 its Kummer curve E/{±1}, E its square product, and K2 the split Kummer surface E /{±1}. The addition law on E gives a large endomorphism ring, which induce endomorphisms of K2. With a view to the practical applications to scalar multiplication on K1, we study the explicit arithmetic of K2.
متن کاملHessian Quartic Surfaces That Are Kummer Surfaces
In 1899, Hutchinson [Hut99] presented a way to obtain a threeparameter family of Hessians of cubic surfaces as blowups of Kummer surfaces. We show that this family consists of those Hessians containing an extra class of conic curves. Based on this, we find the invariant of a cubic surface C in pentahedral form that vanishes if its Hessian is in Hutchinson’s family, and we give an explicit map b...
متن کاملSymplectic Automorphisms on Kummer Surfaces
Nikulin proved that the isometries induced on the second cohomology group of a K3 surface X by a finite abelian group G of symplectic automorphisms are essentially unique. Moreover he computed the discriminant of the sublattice of H(X,Z) which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same of those found for explicit examples. Here we de...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2009
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2008.12.006