Nettet15. nov. 2014 · We prove a new inequality for the Hodge number h^ {1,1} of irregular complex smooth projective surfaces of general type without irrational pencils of … Nettet7. apr. 2024 · This is not obvious to me from the relations they give in the book. Allow me to show you how I have worked out the rest of the elements of the Hodge diamond. Let me write here the properties the book gives for the Hodge numbers. For a Calabi-Yau n-fold we have that -these are eq. (9.10)- (9.12) in the book. h p, 0 = h n − p, 0 h p, q = h q, p ...
arXiv:1612.07193v2 [math.AG] 6 Jun 2024
NettetOn this Wikipedia the language links are at the top of the page across from the article title. Go to top. Nettetwhich of course implies an equality of Hodge polynomials hX(u,v) = hY (u,v) and hence an equality of the Hodge numbers. A similar argument shows that L-equivalent varieties also have the same (motivic) zeta-functions. Thus, Conjecture 1.6 predicts equality of Hodge numbers, zeta-functions (and any other multiplicative motivic invariant whose ... ridding my yard of voles
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Nettet11. apr. 2024 · Once again there are linear combinations of Hodge numbers which can be expressed through the Betti numbers, and are therefore topological invariants. One can now ask for these basic Hodge numbers of Sasaki manifolds the analog of Hirzebruch's question for compact Kähler manifolds which we discussed above. Nettetasymmetry in Hodge numbers, H0(X; 1 X) = 0 while H (X;O X) = C. On the other hand, some other non-K ahler manifolds such as the Iwasawa manifolds do not have a p-adic analogue. The basic cohomological invariants of a compact complex manifold also exist in this setting. The analogue of singular cohomology is etale cohomology Hi et (X;Z ‘), Nettet7. okt. 2024 · I need to assume that X and B are algebraic, compact and smooth. Then, the Hodge numbers of X coincide with the Hodge numbers of F × B. For see this, consider the Grothendieck ring of varieties K 0 ( Var / C). This is the ring generated by varieties over C, quotiented by the "scissor relation" [ X] = [ Y] + [ X ∖ Y] where Y ⊂ X is closed. ridding of impurities