منابع مشابه
Heisenberg-invariant Kummer Surfaces Ii
is the closure of the locus parametrizing H22-invariant quartics with 16 skew lines. The smooth surfaces of this type are parametrized by a non-empty open set N s of N . These surfaces are Kummer surfaces associated to abelian surfaces with a (1,3)–polarization. The action of the Heisenberg group on the Kummer surface corresponds to a level-2 structure on the abelian surface. If A is an abelian...
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 کاملEnriques surfaces covered by Jacobian Kummer surfaces
This paper classifies Enriques surfaces whose K3-cover is a fixed Picard-general Jacobian Kummer surface. There are exactly 31 such surfaces. We describe the free involutions which give these Enriques surfaces explicitly. As a biproduct, we show that Aut(X) is generated by elements of order 2, which is an improvement of the theorem of S. Kondo.
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 کاملSmooth Kummer Surfaces in Projective Three-space
In this note we prove the existence of smooth Kummer surfaces in projective three-space containing sixteen mutually disjoint smooth rational curves of any given degree. Introduction Let X be a smooth quartic surface in projective three-space P. As a consequence of Nikulin’s theorem [6] X is a Kummer surface if and only if it contains sixteen mutually disjoint smooth rational curves. The classic...
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: Proceedings of the Edinburgh Mathematical Society
سال: 2000
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500021015