Many papers have been devoted recently to twisted K-theory as originally defined in [15] and [29]. See for instance the references [2], [23] and the very accessible paper [30]. We offer here a more direct approach based on the notion of “twisted vector bundles”. This is not an entirely new idea, since we find it in [4], [6], [7], [8] and [9] for instance, under different names and from various ...

Quasicoherent sheaves should be thought of as the scheme-theoretic analogs of vector bundles. This analogy might lead one to think that vector bundles over a scheme X should be locally free OX-modules, but this turns out not to be an abelian category, and the category of quasicoherent sheaves contains the category of locally free OX-modules. There are two different different definitions we coul...

We prove sharp bounds on the discriminants of stable rank two sheaves surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion space via tilt stability derived category. then proceed describe surface itself a moduli vector bundles it. Lastly, we give proof Bogomolov inequality for semistable integral all characteristics.

Abstract We show that the derived category of a curve is embedded into moduli space vector bundles on coprime rank and degree. also generalize semiorthogonal decomposition constructed by Narasimhan Belmans-Mukhopadhyay. Finally, we produce one-dimensional family ACM over space.