A constructive approach to Fourier-Mukai transforms for projective spaces via $A_{\infty }$-functors between pretriangulated dg categories

Sebastian Posur

We discuss the following problem: how can an arbitrary Fourier-Mukai transform $\varphi :{\mathrm{D}}^{\mathrm{b}}({\mathbb{P}}^a)\to {\mathrm{D}}^{\mathrm{b}}({\mathbb{P}}^b)$ betw…