Cohomological descent of derived category and Fourier–Mukai to singular rational cohomology

Abstract

This paper presents some nontrivial computational results on derived category and Fourier–Mukai technique in algebraic geometry. In particular, it aims at presenting calculations involving spherical twists as a certain class of Fourier–Mukai functors and its cohomological descent on the singular rational cohomology of smooth projective variety. The purpose of this investigation is to present a new perspective, based upon Fourier–Mukai technique, on solving classical problems involving characteristic classes: in particular, the Chern and the Euler characteristics.