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Results tagged with chern-classes
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user 4790
Characteristic classes associated to complex vector bundles.
4
votes
Accepted
recurrence formula for *i*-th Chern class of $CP^n$
There is no need for a recurrence formula. If $h\in \mathrm H^2(\mathbb C\mathbb P^n, \mathbb Z)$ is the Poincaré dual of a hyperplane section, then $h^i$ generates $\mathrm H^{2i}(\mathbb C\mathbb P^ …
- 27k
12
votes
A simple question about the degree of some vector bundle over rational curve.
Complex curves with anti-holomorphic involutions correspond to real algebraic curves. Your involution has no fixed points, so your curve corresponds to a real curve $C$ of genus 0 with no real points …
- 27k
9
votes
Accepted
Top chern class under finite, unramified, dominant morphism
Yes, it does hold in positive characteristic. You can show that the degree of $c_n(X)$ equals its Euler characteristic with respect to étale cohomology with coefficients in $\mathbb{Q}_{\ell}$, where …
- 27k