Tagged Questions
3
votes
2answers
90 views
Actions of automorphisms in cohomology
Let X be a smooth, projective variety over a field $k \hookrightarrow \mathbb{C}$ and let $g$ be an automorphism of $X$ of finite order. Consider the induced automorphism on the singular cohomology
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1
vote
0answers
30 views
Inequality of numerical invariants of complex algebraic surfaces?
Let $S, T$ be algebraic surfaces over $k=\mathbb{C}$, and $\phi: S \longrightarrow T$ a surjective morphism. Furthermore we have the numerical invariants:
\begin{align*}
q(S) &:= \dim H^1(S, ...
2
votes
1answer
64 views
Exact sequence of four sheaves in Beauville: associated l.e.s.?
This question is about an exact sequence of four sheaves on a smooth projective surface $S$ over $k=\mathbb{C}$, to be found in Beauville: complex algebraic surfaces, theorem I.4, page 3 (second ...
1
vote
1answer
81 views
Torsion elements in H^1 of a complex manifold
If $X$ is a compact complex manifold, the exponential sequence gives an injective map $H^1(X,\mathbb{Z}) \to H^1(X,\mathcal{O}_X)$. I think that this shows that $H^1(X,\mathbb{Z})$ is torsion free.
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