The Universal Kummer Threefold
نویسندگان
چکیده
The universal Kummer threefold is a 9-dimensional variety that represents the total space of the 6-dimensional family of Kummer threefolds in P7. We compute defining polynomials for three versions of this family, over the Satake hypersurface, over the Göpel variety, and over the reflection representation of type E7. We develop classical themes such as theta functions and Coble’s quartic hypersurface using current tools from combinatorics, geometry, and commutative algebra. Symbolic and numerical computations for genus 3 moduli spaces appear alongside toric and tropical methods.
منابع مشابه
Degenerations of ( 1 , 3 ) abelian surfaces and Kummer surfaces
We study degenerations of Kummer surfaces associated to certain divisors in Nieto’s quintic threefold and show how they arise from boundary components of a suitable toroidal compactification of the corresponding Siegel modular threefold. The aim of this paper is to study the degenerations of an interesting class of Kummer surfaces in P in terms of degenerations of the corresponding abelian surf...
متن کاملModularity of Equations D3 and the Iskovskikh Classification
We study conditions for a d –Kummer pullback of a Picard–Fuchs equation in a twisted symmetric square of the universal elliptic curve over X0(N) W to be of type D3. Our main result says that the only possible pairs (N, d) are exactly those for which there exists a Fano threefold with one-dimensional Picard group whose index is d and whose anticanonical degree is 2d2N. We give some modular formu...
متن کاملGeneralised Kummer Constructions and Weil Restrictions
We use a generalised Kummer construction to realise all but one weight four newforms with CM and rational Fourier coefficients in a smooth (non–rigid) Calabi–Yau threefold defined over Q. The Calabi–Yau manifolds are smooth models of quotients of the Weil restrictions of elliptic curves with CM of class number three.
متن کاملBounds of Divided Universal Bernoulli Numbers and Universal Kummer Congruences
Let p be a prime. We obtain good bounds for the p-adic sizes of the coefficients of the divided universal Bernoulli number B̂n n when n is divisible by p− 1. As an application, we give a simple proof of Clarke’s 1989 universal von Staudt theorem. We also establish the universal Kummer congruences modulo p for the divided universal Bernoulli numbers for the case (p − 1)|n, which is a new result.
متن کاملThe Universal Kummer Congruences
Let p be a prime. In this paper, we present detailed p-adic analysis to factorials and double factorials and their congruences. We give good bounds for the p-adic sizes of the coefficients of the divided universal Bernoulli number B̂n n when n is divisible by p−1. Using these we then establish the universal Kummer congruences modulo powers of a prime p for the divided universal Bernoulli numbers...
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:
- Experimental Mathematics
دوره 22 شماره
صفحات -
تاریخ انتشار 2013