K3 surfaces and equations for Hilbert modular surfaces
نویسندگان
چکیده
منابع مشابه
Modular forms and K3 surfaces
For every known Hecke eigenform of weight 3 with rational eigenvalues we exhibit a K3 surface over Q associated to the form. This answers a question asked independently by Mazur and van Straten. The proof builds on a classification of CM forms by the second author.
متن کاملDifferential Equations Satisfied by Bi-modular Forms and K3 Surfaces
We study differential equations satisfied by bi-modular forms associated to genus zero subgroups of SL2(R) of the form Γ0(N) or Γ0(N)∗. In some examples, these differential equations are realized as the Picard–Fuchs differential equations of families of K3 surfaces with large Picard numbers, e.g., 19, 18, 17, 16. Our method rediscovers some of the Lian–Yau examples of “modular relations” involv...
متن کاملDifferential Equations Satisfied by Modular Forms and K3 Surfaces
We study differential equations satisfied by modular forms of two variables associated to Γ1×Γ2, where Γi (i = 1, 2) are genus zero subgroups of SL2(R) commensurable with SL2(Z), e.g., Γ0(N) or Γ0(N)∗ for some N . In some examples, these differential equations are realized as the Picard–Fuchs differential equations of families of K3 surfaces with large Picard numbers, e.g., 19, 18, 17, 16. Our ...
متن کاملK3 surfaces: moduli spaces and Hilbert schemes
LetX be an algebraicK3 surface. Fix an ample divisorH onX ,L ∈ Pic(X) and c2 ∈ Z. Let MH(r;L, c2) be the moduli space of rank r, H-stable vector bundles E over X with det(E) = L and c2(E) = c2. The goal of this paper is to determine invariants (r; c1, c2) for which MH(r;L, c2) is birational to some Hilbert scheme Hilb(X).
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: Algebra & Number Theory
سال: 2014
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2014.8.2297