NettetHodge classes on abelian varieties J.S. Milne November 13, 2024 Abstract Weprove,followingDeligneandAndré,thattheHodgeclassesonabelianvari-etiesofCM … NettetHodge Theory of Compact Oriented Riemannian Manifolds 2.1. Hodge star operator. Let (M;g) be a Riemannian n-manifold. We can consider gas an element of TM TM, and in …
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Nettet23. jan. 2024 · The elements of the image of $ \mathrm{cl}_{ \mathbb{Q} } $ are called rational algebraic Hodge classes of type $ (p,p) $. Hodge conjecture: On a non-singular complex projective variety, any rational Hodge class of type $ (p,p) $ is algebraic, i.e : in the image of $ \mathrm ... Nettet2. jul. 2003 · The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard–Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global … how to check arp entry in fortigate firewall
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Nettetby taking the cohomology class [ZnZsing] 2 H2k(XnZsing;Z) of the closed complexsubmanifold Z nZsing ‰ X nZsing and by observing that H2k(X nZsing;Z) »= H2k(X;Z). The class [Z] is an integral Hodge class.This can be seen using Lelong’s theorem, showing that the current of integration over ZnZsing is well deflned and … Nettet14. apr. 2024 · Non-abelian Hodge theory and higher Teichmüller spaces. Abstract: Non-abelian Hodge theory relates representations of the fundamental group of a compact Riemann surface X into a Lie group G with holomorphic objects on X known as Higgs bundles, introduced by Hitchin more than 35 years ago. Nettetthe usual cycle class map CH∗(X)⊗Q → Hdg∗(X,Q) to the group of rational Hodge classes of all degrees. Therefore, the Hodge conjecture in all degrees for X is equivalent to the Hodge conjecture for Dperf(X). The integral Hodge conjectures for X and Dperf(X) are more subtly, but still very closely, related (Proposition 5.16). michelle franke facebook