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Results tagged with at.algebraic-topology
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user 1784
Homotopy theory, homological algebra, algebraic treatments of manifolds.
38
votes
Accepted
Example Wanted: When Does Čech Cohomology Fail to be the same as Derived Functor Cohomology?
Q1: A very simple example is given in Grothendieck's Tohoku paper "Sur quelques points d'algebre homologique", sec. 3.8. Edit: The space is the plane, and the sheaf is constructed by using a union of …
- 4,492
7
votes
Accepted
Applications of Faber's conjecture
Numerical evidence, from computing the cases $g=2,3,\dots$, eventually $g\le 15$, and seeing the symmetry in the numbers $\dim R_g^n$. I recall Carel saying he made the conjecture when $g$ was still …
- 13.1k
7
votes
Classification of simply connected smooth projective varieties?
That is way too ambitious, I think, considering what is known about classification of algebraic varieties. Ignoring the trivial, for these purposes, case of curves, the next and best studied case is a …
- 13.1k
12
votes
What is the Euler characteristic of a Hilbert scheme of points of a singular algebraic curve?
The same formula holds for $\chi(X^{[n]})$ of any topological space for which $\chi(X)$ is defined and behaves in the expected way for unions, Cartesian products, and quotients by a finite free action …
- 13.1k