2024 Systems of hodge bundles and uniformization

Systems of hodge bundles and uniformization

Author: nvos

August undefined, 2024

WebDefine a system of Hodge bundles E on X to be a collection of holomorphic vector bundles (p+q= w, the weight of E), together with holomorphic maps x: E p, q ~ E p - 1, q + 1 f~l x … WebApr 8, 2024 · April 2024; Authors: Jie Zhou

JOURNAL OF THE

WebYang-Mills Theory and Uniformization CARLOS T. SIMPSON Princeton University, Princeton, NJ 08544, U.S.A. (Received: 9 September 1987) Abstract. We define a notion of a stable system of Hodge bundles. ... category of systems of Hodge bundles: if V is a variation then the components vP'q---~A O" I(vP'q) of the connection give holomorphic ... shivansh outsourcing

ISOMONODROMY, STABILITY, AND HODGE THEORY

WebSimpson deﬁned a principal system of Hodge bundles associated to (Ω1 X ⊕ OX,θ) whose second Chern class vanishes by [Sim88, Proposition 9.8]. By [Sim88, Proposi-tion 8.2], this gives rise to a principal variation of Hodge structures on the universal covering ofX, whose … WebIn physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a … Weba system of Hodge bundles is a direct sum of metrics on the Ep q, and any such metric gives rise to a connection which preserves the associated indefinite form. We try to solve the … r 50 batt insulation thickness

American Mathematical Society :: Homepage

WebThe Riemann curvature tensor is also the commutator of the covariant derivative of an arbitrary covector with itself:;; =. This formula is often called the Ricci identity. This is the classical method used by Ricci and Levi-Civita to obtain an expression for the Riemann curvature tensor. This identity can be generalized to get the commutators for two … WebDec 13, 2024 · Hodge theory, the so-called sys tem of Hodge bundles (E, θ), to b e the associated graded Higgs bun- dle of a polarized variation of Hodge structures. These theories are of fundamental i ... r 50 insulationWebcontext of Higgs bundles, and as an application he proved a uniformization theorem which characterizes complex projective manifolds and quasi-projective curves whose universal … r-50m 5.1.4 home theater system

"WebA stable system of Hodge bundles has a Hermitian-Yang-Mills metric and, if certain Chern classes vanish, this gives a complex variation of Hodge structure. We use these ideas to … " - Systems of hodge bundles and uniformization

Systems of hodge bundles and uniformization

http://ydeng.perso.math.cnrs.fr/uniformization.pdf WebHodge bundles. Step 2. We generalize the result in Step 1 to the context of principal bundles.Fix a Hodge group G0. Following Simpson again, we deﬁne a principal system of log Hodge bundles (P,τ)on log pairs (X,D) with the structure group K ⊂ G, where G is the complexiﬁcation of G0. Based on the result in Step 1 together with some

Did you know?

WebFrom a variation of Hodge structure, a system of Hodge bundles is obtained in a natural way: different com- ponents of the connection D give holomorphic structures a on the VP ,q, and holomorphic maps 0. If a variation of Hodge structure comes from a family of varieties, the associated system of Hodge bundles is easier to calculate than WebStability of Hodge bundles 22 4. Families of Abelian varieties 33 5. The structure of U˜ in Theorem 5 36 ... type inequalities only for the Hodge bundles of irreducible local sub-systems. Theorem 1. ... apply Yau’s uniformization theorem [Y93], recalled in 1.4. It implies. 4 ECKARTVIEHWEGANDKANGZUO

Web[46] C. T. Simpson, Systems of Hodge bundles and uniformization, doctoral dissertation, Harvard University (1987). [47] C. T. Simpson, Constructing variations of Hodge structure … WebSimpson Variations of Hodge using Yang-Mills - math.mit.edu

WebSimpson Variations of Hodge using Yang-Mills - math.mit.edu WebSimpson, Systems of Hodge bundles and uniformization. Harvard thesis,1987. 7. C. ... Higgs bundles and local systems on Riemann surfaces. Lecture notes ...

WebHiggs bundles have a rich structure and play a role in many diﬀerent areas including gauge theory, Kähler and hyperkähler geometry, surface group representa- tions, integrable systems, nonabelian Hodge theory, the Deligne–Simpson problem on products of matrices, and (most recently) mirror symmetry and Langlands duality.

WebThe non-abelian Hodge theory identifies moduli spaces of representations with moduli spaces of Higgs bundles through solutions to Hitchin's selfduality equations. On the one hand, this enables one to relate geometric structures on surfaces with algebraic geometry, and on the other hand, one obtains interesting hyper-Kähler metrics on the ... shivansh name logoWebMar 30, 2024 · The adoption of this approach has grown significantly over the last decade. In 2024 over 1,000 hospitals and over 700 physician groups participated in the voluntary … shivansh oxfordWebvariation of Hodge structure of rank 2, arising from uniformization (see e.g. [Sim88, bottom of p. 870]). As local systems which arise from geometry satisfy the hypotheses of Theorem 1.2.4, we have: Corollary 1.2.6. Let (C, x 1, , xn) be an analytically very general hyperbolic n-pointed curve of genus g. If f : X !C nfx 1, , xngis a smooth ... r 50 pink round pillWebDec 5, 2024 · Systems of Hodge bundles and uniformization, Ph.D. Thesis, Harvard Univ., Cambridge, MA, 1987; J. Amer. Math. Soc. 1 (1988), no. 4, 867–918; MR90e:58026, doi. … r50 led reflector bulbsWebC1-bundle of Ewith a new holomorphic structure, ris an integrable connection r: H!H 1 X; Filis a Hodge ltration, that is, a nite decreasing ltration satisfying Gri ths transversality and is a horizontal bilinear form satisfying the Hodge-Riemann bilinear relation. By taking the grading of the Hodge ltration, one obtains shivansh outsourcing private limitedWebwork, one is that the system of Hodge bundles are of Calabi-Yau type and theotherisalocalTorelli-typetheorem,seesection5of[8]. 2 Systems of Hodge bundles over … r 5.0 insulation battsWebDec 13, 2024 · Abstract Using classical results from Hodge theory and more contemporary ones valid for complex projective varieties with Kawamata log terminal (klt) singularities, we deduce necessary and... shivansh patel