Hilbert modular surface

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August undefined, 2024

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 … Webis the complete understanding of how the corresponding Hilbert modular surface (Z (D)) ts into the Enriques-Kodaira rough classi cation of surfaces, which classi es a surface X in terms of its Hodge numbers hi;j = dimHj(X; i). Such a surface is regular and simply connected, hence is either

Igusa class polynomials, embeddings of quartic CM fields, and ...

Webthe modular curve into the Hilbert modular sur-face. We have SL2(Z) ,→ SL2(O F) and h,→ h × h giving rise to SL2(Z)\h,→ SL2(O F)\(h × h). More generally, we can work with a … http://www.numdam.org/item/AST_1976__32-33__151_0.pdf chudleigh knighton pre-school

Hilbert modular surfaces and the classification of algebraic …

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. WebHere we describe classical theta functions and Satake compactiﬁcations as well as provide some examples of mod- uli spaces of abelian surfaces having a real multiplication (RM) structure (Hilbert modular surfaces). Chapter 2 is an overview of Humbert surfaces. 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 ... chudleigh knighton post office

Borcherds products and arithmetic intersection theory on Hilbert ...

Foliations of Hilbert modular surfaces

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 … 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 … chudleigh knighton newsWebsurface 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 … destiny 2 phenotypic plasticity robes

"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 … " - Hilbert modular surface

Hilbert modular surface

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 … 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.

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WebOct 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 ... 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 …

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 all n i are non-negative, and it is called positive if it is non-negative and not zero. ... Hilbert Modular Surfaces . and 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.

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 … 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

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-

Webthe 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 destiny 2 phogothWebHilbert modular surfaces, Surfaces modulaires de Hilbert, 31.14 number theory, Hilbert-Fläche, Hilbertsche Modulfläche, Hilbert modulaire oppervlakken, Surfaces, Algebraic, … destiny 2 phoenix protocol build 2021WebON HILBERT MODULAR SURFACES By TONGHAI YANG Abstract. In this paper, we obtain an explicit arithmetic intersection formula on a Hilbert modular surface between the … destiny 2 phry\u0027zhia the insatiableWebOver 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 … chudleigh knighton primary school term datesWebdiﬁerent 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 ... chudleigh knighton pre schoolWebMar 23, 2024 · The surface is called the Hilbert modular surface. In this paper we mainly consider the surface. which is the moduli space of principally polarized abelian varieties of genus 2 with real multiplication. In order to prove the rationality of … chudleigh knighton mapWebInoue's surface (cfs Inoue'. s lecture at the Vancouver International Congress). Let G(M) act on H x C , the actio n being given by the same formula as before. ... HILBERT MODULAR SURFACES 1 2 - (K - 2e) - Sig n is 0 b signatury the e theorem an,d we can calculate this destiny 2 phoenix protocol how to get