Rational double points on supersingular K3 surfaces
نویسنده
چکیده
We investigate configurations of rational double points with the total Milnor number 21 on supersingular K3 surfaces. The complete list of possible configurations is given. As an application, we also give the complete list of extremal (quasi-)elliptic fibrations on supersingular K3 surfaces.
منابع مشابه
On Normal K3 Surfaces
We determine all possible configurations of rational double points on complex normal algebraic K3 surfaces, and on normal supersingular K3 surfaces in characteristic p > 19.
متن کاملDynkin Diagrams of Rank 20 on Supersingular K3 Surfaces
We classify normal supersingular K3 surfaces Y with total Milnor number 20 in characteristic p, where p is an odd prime that does not divide the discriminant of the Dynkin type of the rational double points on Y .
متن کاملKummer Surfaces for the Selfproduct of the Cuspidal Rational Curve
The classical Kummer construction attaches to an abelian surface a K3 surface. As Shioda and Katsura showed, this construction breaks down for supersingular abelian surfaces in characteristic two. Replacing supersingular abelian surfaces by the selfproduct of the rational cuspidal curve, and the sign involution by suitable infinitesimal group scheme actions, I give the correct Kummer-type const...
متن کاملSupersingular K3 Surfaces in Odd Characteristic and Sextic Double Planes
We show that every supersingular K3 surface is birational to a double cover of a projective plane.
متن کاملSupersingular K3 Surfaces in Characteristic 2 as Double Covers of a Projective Plane
For every supersingular K3 surface X in characteristic 2, there exists a homogeneous polynomial G of degree 6 such that X is birational to the purely inseparable double cover of P defined by w = G. We present an algorithm to calculate from G a set of generators of the numerical Néron-Severi lattice of X. As an application, we investigate the stratification defined by the Artin invariant on a mo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 73 شماره
صفحات -
تاریخ انتشار 2004