منابع مشابه
Modular Curves, Modular Surfaces, and Modular Fourfolds
We begin with some general remarks. Let X be a smooth projective variety of dimension n over a field k. For any positive integer p < n, it is of interest to understand, modulo a natural equivalence, the algebraic cycles Y = ∑ j mjYj lying on X, with each Yj closed and irreducible of codimension p, together with codimension p + 1 algebraic cycles Zj = ∑ i rijZij lying on Yj , for all j. There is...
متن کاملAlgebraic surfaces
The previous result shows that a minimal model for surface always exists and that a surface X is minimal if and only if X has no (−1)curve. Hence we may and we usually do assume that X is minimal. However, the criterion by (−1) curve only valid for surface. We might prefer to have a criterion which is also valid for higher dimension. If X has a (−1)-curve E, then KX .E = −1 < 0. Thus if KX is n...
متن کاملModular Diagonal Quotient Surfaces
Notes: 1) The modular diagonal quotient surfaces as defined above may be viewed as a special case of the general diagonal quotient surfaces studied in Kani/Schanz[7]. 2) The inclusions of subsgroups {1} ≤ ∆αε ≤ G × G induce finite morphisms (both of degree m = |G|) YN Φ → ZN,ε Ψ → Y1 ' P × P. Moreover, by using Shimura’s canonical model X(N)/Q, it can be shown that all these varieties have cano...
متن کاملModular Diagonal Quotient Surfaces
The main objective of this paper is to analyze the geometry of the modular diagonal quotient surface ZN,ε = ∆ε\(X(N) × X(N)) which classifies pairs of elliptic curves E1 and E2 together with an isomorphism of “determinant ε” between their associated modular representations mod N . In particular, we calculate some of the numerical invariants of its minimal desingularization Z̃N,ε such as its Bett...
متن کاملFoliations of Hilbert modular surfaces
The Hilbert modular surface XD is the moduli space of Abelian varietiesA with real multiplication by a quadratic order of discriminant D > 1. The locus where A is a product of elliptic curves determines a finite union of algebraic curves XD(1) ⊂ XD. In this paper we show the lamination XD(1) extends to an essentially unique foliation FD of XD by complex geodesics. The geometry of FD is related ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1961
ISSN: 0002-9327
DOI: 10.2307/2372959