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Characteristic classes associated to complex vector bundles.

10 votes
3 answers
2k views

on chern classes and Riemann Roch theorem for torsion-free sheaves on singular (possibly mul...

I'm looking for a definition of Chern class (at least the first one) for a torsion-free sheaf $F$ (not necessarily locally free) on a singular curve (for simplicity can assume all the singularities …
Dmitry Kerner's user avatar
2 votes
1 answer
512 views

Looking for an inequality between Chern and Todd classes (something in style of Bogomolov-Mi...

Consider a smooth projective surface $S\subset\Bbb P^N_{\Bbb C}$ which is a complete intersection of hypersurfaces of degrees $(d_1,..,d_{k\ge2})$ with $d_i\ge2$ for all i. Is it true that for such s …
Dmitry Kerner's user avatar