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Results tagged with at.algebraic-topology
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user 8621
Homotopy theory, homological algebra, algebraic treatments of manifolds.
3
votes
Cohomology of Hypersurface complement
Griffiths (On the periods of certain rational integrals. I, II. Ann. of Math. 90 (1969), 460-495 & 90 (1969), 496–541.) gave a procedure to calculate the Hodge numbers of Y. Let $S=\mathbf{C}[x_0,\dot …
- 3,338
2
votes
$b_2$ of the blow up of a complex $3$-fold in a curve
I am not sure whether $b_2(V')-b_2(V)=1$ always holds. Anyway, in the book of Peters and Steenbrink you can find "the Mayer-Vietoris sequence of the discriminant square". If $E$ is the exceptional div …
- 3,338
5
votes
Cohomology of complete intersections
If $X$ is smooth then Lefschetz' hyperplane theorem and Poincaré duality yield that $H^i(X,\mathbb{Z})=H^i(\mathbb{P}^n,\mathbb{Z})$ for $i=0,\dots, 2\dim X$, $i\neq \dim X$.
(This is proven in Dimca' …
- 3,338