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Full-Text Articles in Algebraic Geometry
On Hilbert Modular Threefolds Of Discriminant 49, Lev A. Borisov, Paul E. Gunnells
On Hilbert Modular Threefolds Of Discriminant 49, Lev A. Borisov, Paul E. Gunnells
Paul Gunnells
Let K be the totally real cubic field of discriminant 49 , let \fancyscriptO be its ring of integers, and let p⊂\fancyscriptO be the prime over 7 . Let Γ(p)⊂Γ=SL2(\fancyscriptO) be the principal congruence subgroup of level p . This paper investigates the geometry of the Hilbert modular threefold attached to Γ(p) and some related varieties. In particular, we discover an octic in P3 with 84 isolated singular points of type A2 .
Mixed Discriminants, Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein, Sandra Di Rocco, Bernd Strumfels
Mixed Discriminants, Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein, Sandra Di Rocco, Bernd Strumfels
Eduardo Cattani
No abstract provided.
Toric Modular Forms And Nonvanishing Of L-Functions, Lev A. Borisov, Paul E. Gunnells
Toric Modular Forms And Nonvanishing Of L-Functions, Lev A. Borisov, Paul E. Gunnells
Paul Gunnells
In a previous paper \cite{BorGunn}, we defined the space of toric forms $\TTT(l)$, and showed that it is a finitely generated subring of the holomorphic modular forms of integral weight on the congruence group Γ1(l). In this article we prove the following theorem: modulo Eisenstein series, the weight two toric forms coincide exactly with the vector space generated by all cusp eigenforms f such that L(f,1)≠0. The proof uses work of Merel, and involves an explicit computation of the intersection pairing on Manin symbols.
Evaluation Of Dedekind Sums, Eisenstein Cocycles, And Special Values Of L-Functions, Pe Gunnells, R Sczech
Evaluation Of Dedekind Sums, Eisenstein Cocycles, And Special Values Of L-Functions, Pe Gunnells, R Sczech
Paul Gunnells
We define higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums as well as Zagier's sums, and we show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications. First, we show how to express special values of partial zeta functions associated to totally real number fields in terms of these sums via the Eisenstein cocycle introduced by R. Sczech. Hence we obtain a polynomial time algorithm for computing these special values. Second, we show how to use our techniques to compute certain special values of the Witten zeta function, and we compute some …
A Smooth Space Of Tetrahedra, E Babson, Pe Gunnells, R Scott
A Smooth Space Of Tetrahedra, E Babson, Pe Gunnells, R Scott
Paul Gunnells
This is the pre-published version harvested from ArXiv. We construct a smooth symmetric compactification of the space of all labeled tetrahedra in 3.
Elliptic Functions And Equations Of Modular Curves, Lev A. Borisov, Paul E. Gunnells, Sorin Popescu
Elliptic Functions And Equations Of Modular Curves, Lev A. Borisov, Paul E. Gunnells, Sorin Popescu
Paul Gunnells
Let P≥5 be a prime. We show that the space of weight one Eisenstein series defines an embedding into P(p−3)/2 of the modular curve X1(p) for the congruence group Γ1(p) that is scheme-theoretically cut out by explicit quadratic equations.