Hilbert modular surface

Author: jkzc

August undefined, 2024

Weba suitable regular model of the Hilbert modular surface. We show that the generating series of their classes in the arithmetic Chow ring is a holomorphic modular form (of the same level, weight, and character as in the case of Hirzebruch and Zagier). The main result of our work is that the product of this generating series with the square WebSiegel modular form; Hilbert modular surface; References. Jan H. Bruinier: Hilbert modular forms and their applications. Paul B. Garrett: Holomorphic Hilbert Modular Forms. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1990. ISBN 0-534-10344-8; Eberhard Freitag: Hilbert Modular Forms. Springer-Verlag. ISBN 0-387-50586-5

Hilbert modular surfaces and the classification of algebraic …

WebAbstract. This chapter is devoted to complex abelian surfaces whose endomorphism ring contains an order from a real quadratic field. The moduli spaces of such abelian surfaces are Hilbert modular surfaces. Since the moduli spaces of polarized complex abelian varieties are Siegel modular varieties we find natural maps of Hilbert modular surfaces ... WebDec 23, 2024 · In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is one of the surfaces obtained by taking a quotient of a product of two copies of the upper … eamonn torsney

The rings of Hilbert modular forms for Q(29) and Q(37)

Webdiﬁerent type in a Hilbert modular surface over Z, arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles associated to non-biquadratic quartic CM ﬂelds. They intersect properly and have a conjectured arithmetic intersection formula [BY]. The main purpose of this paper is to prove the conjectured formula under a minor technical ... WebIn the special case of RM-5, the Hilbert modular surface Y(5) = Y (5) is a rational surface, i.e., birational to P2 m;n(C). Hence to proveTheorem 1.1, it su ces to show that the vanishing of the Mestre obstruction at a rational point (m;n) in Y(5) is generically equivalent to the condition that m2 5n2 5 = u2 5v2 for some u;v2Q. This WebSep 16, 2012 · We outline a method to compute rational models for the Hilbert modular surfaces Y_ {-} (D), which are coarse moduli spaces for principally polarized abelian surfaces with real multiplication by the ring of integers in Q (sqrt {D}), via moduli spaces of elliptic K3 surfaces with a Shioda-Inose structure. eamonn trotter

K3 surfaces and equations for Hilbert modular surfaces

WebSep 16, 2012 · Abstract: We outline a method to compute rational models for the Hilbert modular surfaces Y_{-}(D), which are coarse moduli spaces for principally polarized … WebSome remarks on Hilbert modular surfaces of general type. To appear Download references Authors and Affiliations Mathematisches Institut der Universität, Wegelerstraße 10, D-5300, Bonn, Federal Republic of Germany F. Hirzebruch Mathematisch Instituut, Rijksuniversiteit te Leiden, Wassenaarseweg 80, Leiden, The Netherlands A. Van de Ven eamonn treacyWebcertain 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 ... eamonn thompson sligo

"WebThe Hilbert modular group Γ acts on H2 by fractional linear transformations: a b c d z = az 1 +b cz 1 +d, a0z 2 0 c0z 2 +d0 (12) The quotient Y = Y(Γ) = Γ\H2 (13) is a complex surface, … " - Hilbert modular surface

Hilbert modular surface

WebHilbert modular surfaces An example: Y−(17). Applications Method/proof 2/31 Ellipticcurves An elliptic curve over Cis the set of solutions to an equation y2= x3+Ax+B with A,B∈ Cwith … WebFoliations of Hilbert modular surfaces Curtis T. McMullen∗ 21 February, 2005 Abstract The Hilbert modular surface XD is the moduli space of Abelian varieties A with real …

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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. … Websurface X, which is always supposed to be connected. Such a divisor is a finite sum ~ n i Ci, n~eZ, where C~ is an irreducible algebraic curve on X. The divisor is called non-negative if …

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 ... WebJun 25, 2024 · We study the Iwasawa main conjecture for quadratic Hilbert modular forms over the p-cyclotomic tower. Using an Euler system in the cohomology of Siegel modular varieties, we prove the "Kato divisibility" of the Iwasawa main conjecture under certain technical hypotheses.

WebJan 3, 2024 · representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps holds, this Euler system is … WebOver the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular …

WebHilbert modular surfaces and the classification of algebraic surfaces. Andreotti, A.: On the complex structures of a class of simply connected manifolds. In: Algebraic geometry and …

WebThe Hilbert Modular Group for the Field Q(I/13) 99 On the other hand, the Chern class c 1 of Y can be represented by a differential form 71 +72, where Y2 represents in HZ(Y) the Poincar6 dual of the homology class of the cusp resolutions, and where 71 has support disjoint from the cusp resolutions and satisfies … csp toolWebthe Hilbert modular surface XD is populated by inﬁnitely many modular curves FN [Hir], [vG]. The endomorphism ring of a generic Abelian variety in FN is a quaternionic order R of discriminant N2. In general FN can be reducible, and R is not determined up to iso-morphism by N. In §3 we introduce a reﬁnement FN(ν) of the traditional cspt profesionalesWebThe surface has 10 Eckardt points where 3 lines meet, given by the point (1 : −1 : 0 : 0 : 0) and its conjugates under permutations. Hirzebruch (1976) showed that the surface … eamonn twomey step changeWebThe Hilbert modular surface Σ is abundantly populated by modular curves (Shimuracurves), parameterizing Abelian varieties with an action of aquater-nion algebra [vG, §V]. However … csptray.exeWebOct 1, 2024 · Hilbert modular forms can be restricted to the Hirzebruch-Zagier cycles of [16] to produce elliptic modular forms for Γ 0 (n). Recall that the Hirzebruch-Zagier cycle of discriminant n is the set T n ⊆ H × H of all points ( τ 1 , τ 2 ) that satisfy an equation of the form a τ 1 τ 2 + λ τ 1 + λ ′ τ 2 + b = 0 for some a , b ∈ Z ... eamonn \u0026 ruthWebNov 15, 2024 · We construct an Euler system—a compatible family of global cohomology classes—for the Galois representations appearing in the geometry of Hilbert modular … csp tourbillonWebMODCLT is your premier Charlotte system-built home builder. Our company is the first to bring modular homes to Charlotte. When building system-built homes, we use the same … csp top 200