WebJan 1, 1979 · Let us denote by BY the union of all curves on the Hilbert modular surface Y that arise from the resolution of singularities. The following important proposition is a slight generalisation of a similar one we gave in [3]. PROPOSITION 5. Let C be a non-singular rational curve on the Hilbert modular surface Y. In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group. More generally, a Hilbert modular variety is an algebraic variety obtained by taking a quotient of a … See more If R is the ring of integers of a real quadratic field, then the Hilbert modular group SL2(R) acts on the product H×H of two copies of the upper half plane H. There are several birationally equivalent surfaces related to this … See more • Hilbert modular form • Picard modular surface • Siegel modular variety See more Hirzebruch (1953) showed how to resolve the quotient singularities, and Hirzebruch (1971) showed how to resolve their cusp singularities. See more The papers Hirzebruch (1971), Hirzebruch & Van de Ven (1974) and Hirzebruch & Zagier (1977) identified their type in the classification of algebraic surfaces. Most of them are See more • Ehlen, S., A short introduction to Hilbert modular surfaces and Hirzebruch-Zagier cycles (PDF) See more
EULER SYSTEMS FOR HILBERT MODULAR SURFACES
WebNov 8, 2013 · MotivationThe Hilbert Modular GroupResolution of the CuspsSignatures The narrow class group C+ = fractional ideals modulo strict equivalence: a ˘b ,a = b for some totally positive 2F For a fractional ideal a of F, a 7!a 2 induces a homomorphism Sq: C !C+ where C+ is the narrow class group of F Hence to each cusp corresponding to an ideal … WebThe Hilbert modular surface Σ is abundantly populated by modular curves (Shimuracurves), parameterizing Abelian varieties with an action of aquater-nion algebra [vG, §V]. However these curves are covered by the graphs of isometries, so we have: Corollary 10.2 The Teichmu¨ller curve V ⊂ Σ is not a modular curve. harbour towne ocmd rentals
Foliations of Hilbert modular surfaces
Webcertain Hilbert modular surface: we have V ˆ ˘= (H H)= ˆ M2; where is commensurable to SL2(OK), and parameterizes those X ad-mitting real multiplication by a given order in K. Let us say ! is a Weierstrass form if its zero divisor is concentrated at a single point. By imposing this additional condition, we reduce from surfaces to curves and ... WebDe ne Hilbert modular varieties, their cusps and fundamental domains for arbi-trary totally real number elds K=Q ([vdG88, Chapter I.1.,I.3.]). Then prove the structure of elliptic xed points ([vdG88, Chapter I.5.]), introduce the quotients Hn= (as analytic spaces) and de ne Hilbert modular forms ([vdG88, Chapter I.6.]). Finally, identify ... WebOct 14, 2003 · Borcherds products and arithmetic intersection theory on Hilbert modular surfaces. We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying … chandra johnson obit