Determinantal quartics and the computation of the Picard group
نویسندگان
چکیده
We test the methods for computing the Picard group of a K3 surface in a situation of high rank. The examples chosen are resolutions of quartics in P having 14 singularities of type A1. Our computations show that the method of R. van Luijk works well when sufficiently large primes are used.
منابع مشابه
Kummer surfaces and the computation of the Picard group
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. Using the theory of abelian varieties, in this case the Picard group may be computed directly. Our experiments show that the upper bounds provided by R. van Luijk’s method are sharp when sufficiently large primes are used. In fact, there are many pri...
متن کاملBounding Picard numbers of surfaces using p-adic cohomology
Motivated by an application to LDPC (low density parity check) algebraic geometry codes described by Voloch and Zarzar, we describe a computational procedure for establishing an upper bound on the arithmetic or geometric Picard number of a smooth projective surface over a finite field, by computing the Frobenius action on p-adic cohomology to a small degree of p-adic accuracy. We have implement...
متن کاملررسی شرط پیکارد در مسأله انتقال به سمت پائین در تعیین ژئوئید بدون استفاده از روش استوکس
The problem of downward continuation of the gravity field from the Earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying Stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the Earth’s surface. Downward continuation is a...
متن کاملK3 Surfaces of Picard Rank One and Degree Two
Examples 1. A K3 surface of degree two is a double cover of P, ramified in a smooth sextic. K3 surfaces of degree four are smooth quartics in P. A K3 surface of degree six is a smooth complete intersection of a quadric and a cubic in P. And, finally, K3 surfaces of degree eight are smooth complete intersections of three quadrics in P. The Picard group of a K3 surface is isomorphic to Zn where n...
متن کاملSymplectic bundles on the plane, secant varieties and Lüroth quartics revisited
Let X = P × P embedded with O(1, 2). We prove that its (n + 1)-secant variety σn+1(X) is a hypersurface, while it is expected that it fills the ambient space. The equation of σn+1(X) is the symmetric analog of the Strassen equation. When n = 4 the determinantal map takes σ5(X) to the hypersurface of Lüroth quartics, which is the image of the Barth map studied by LePotier and Tikhomirov. This hi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010