Hilbert modular surface

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August undefined, 2024

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WebI Broad goal: Express geometric invariants of a Hilbert modular surface Y in terms of arithmetic invariants of the number eld and the group . I Goal: Understand Theorem IV.2.5 of van der Geer, which gives a formula for the Chern numbers of Y. Chern number = volume term + resolution terms from resolving cusps and cyclic quotient singularities. 2/25 Webon Hilbert modular surfaces Jan H. Bruinier, Jose I. Burgos Gil, and Ulf Kuhn¨ October 25, 2005 Abstract We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coeﬃcients of an elliptic modular form of weight two. Moreover, we determine the arithmetic self- how to silkscreen t shirts

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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. 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 ... 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 … 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 … nov. 6–12 national diabetes education week

Equations for Hilbert modular surfaces

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 … 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 nov. 7 2022 powerball numbersWebThe 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. how to silkscreen shirts

"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 ... " - Hilbert modular surface

Hilbert modular surface

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 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 …

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WebThe key to a great poured in place rubber surface that lasts is expert installation and quality products, at PlaygroundSurfacing.com; we provide both. We are able to do intricate … 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 …

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 … WebDetermining Building Restrictions for a Specific Property: If a property is located in a subdivision, the maximum built upon area allocated to that property can be obtained from …

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 … WebThe 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 …

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 …

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. how to silkscreen your own shirtsIn 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 nov. 7 powerball numbersWebDe 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 ... nov. 7 2022 powerball winnerWebNov 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 … how to silky my hair at homeWebOct 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 ... nov. 7 on this dayWeba 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 how to silkscreen your own t shirtsWebIn logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of … nov. 7 2022 winning powerball numbers