Nettet25. jan. 2005 · The Hard Lefschetz Theorem (HLT) and the Hodge-Riemann bilinear relations (HRR) hold in various contexts: they impose restrictions on the cohomology algebra of a smooth compact Kahler manifold; they… 30 Highly Influenced PDF View 3 excerpts, cites background and methods Hard Lefschetz properties, complete … NettetWe will not explain in these notes the proofs of the main theorems (the existence of Hodge decomposition, the Hodge-Riemann bilinear relations), as this is well-known and presented in [44] I, [22], but rather give a number of applications of the formal notion of Hodge structures, and other objects, like Mumford-Tate groups, Hodge classes, which …
COMBINATORIAL LEFSCHETZ THEOREMS BEYOND POSITIVITY
NettetWe study horizontal subvarieties of a Griffiths period domain . If is defined by algebraic equations, and if is also invariant under a large discrete subgroup in an appropriate sense, we prove that is a Hermitian s… Using the Riemann bilinear relations, in this case called Hodge Riemann bilinear relations, it can be substantially simplified. A polarized Hodge structure of weight n consists of a Hodge structure ( H Z , H p , q ) {\displaystyle (H_{\mathbb {Z} },H^{p,q})} and a non-degenerate integer bilinear form Q on H Z {\displaystyle … Se mer In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Se mer • The Tate–Hodge structure $${\displaystyle \mathbb {Z} (1)}$$ is the Hodge structure with underlying $${\displaystyle \mathbb {Z} }$$ module given by $${\displaystyle 2\pi i\mathbb {Z} }$$ (a … Se mer The machinery based on the notions of Hodge structure and mixed Hodge structure forms a part of still largely conjectural theory of motives envisaged by Alexander Grothendieck. Arithmetic information for nonsingular algebraic variety X, encoded by … Se mer Definition of Hodge structures A pure Hodge structure of integer weight n consists of an abelian group $${\displaystyle H_{\mathbb {Z} }}$$ and a decomposition of its … Se mer It was noticed by Jean-Pierre Serre in the 1960s based on the Weil conjectures that even singular (possibly reducible) and non-complete algebraic varieties should admit 'virtual Betti numbers'. More precisely, one should be able to assign to any algebraic variety … Se mer A variation of Hodge structure (Griffiths (1968), Griffiths (1968a), Griffiths (1970)) is a family of Hodge structures parameterized by a … Se mer Hodge modules are a generalization of variation of Hodge structures on a complex manifold. They can be thought of informally as … Se mer connecting new tv to dish network
Hodge theory and the topology of compact K˜ahler and complex …
Nettet6 E. Cattani We recall that a Hodge structure of weight d on a real vector space H is a decomposition of its complexification HC, HC = p+q=d Hp,q (2.2) such that Hp,q = Hq p. A Hodge structure of weight d on H is said to be polarized if there exists a real bilinear form Q of parity (−1)d, such that the Hermitian form Qh(.,. i−d Q(.,.) makes the … NettetIn the rst lecture we discuss what it means for a variety to admit a (strong) Hodge de-composition on its cohomology, and we introduce the category of Hodge structures. In … Nettetinequalities etc.) either could be deduced from the Hodge–Riemann bilinear rela-tions, or find their analogs for algebraic varieties that generalize the Hodge–Riemann 2000 … edinburgh college term dates 2022/23