Compactification of Arithmetic Quotients of Bounded Symmetric Domains

Siegel Modular Forms and Their Applications

“…By Chow's lemma it is then a projective variety. The following theorem is a special case of a general theorem due to Baily and Borel, [8].…”

“…In principle our database allows for the calculation of the traces of the Hecke operators T (p) with p ≤ 37 on the spaces S j,k for all values j, k. In the cases at hand these numbers tend to be 'smooth', i.e., they are highly composite numbers as we illustrate with the two 1-dimensional spaces S j,k for (j, k) = (8,8) and (12,6) (where the trace equals the eigenvalue of T (p)).…”

Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication

“…4 Hence the singularities of W q × F 3 / α 2 , which result by the exceptional divisor of W q → W q , are locally given by the product of B 1 with a singularity of the type A 3,2 . Now we construct a desingularisation of W × F 3 / α 2 , which is a CMCY family of 3-manifolds.…”

“…(see [13], 2.1.2. (or [4] for the construction of the structure of a complex variety)) Next one needs the ring of finite adèles 7 , which is given by…”

“…Hence here one can not formulate a relative version of the Castelnuovo Theorem as in Proposition 9.1.2. 4 The singular locus of W q is contained in W q ∩ {z 5 = 1}. Thus one can calculate the desingularization with the usual equations z i t j = z j t i for i, j = 1, 2, 3.…”