On taking twists of Fourier-Mukai transforms

Details On taking twists of Fourier-Mukai transforms On taking twists of Fourier-Mukai transforms

2010-04-18

arxiv.org/abs/1004.3052v2

Mathematics

Algebraic Geometry

21 pages; v2: A reference corrected in Section 2

Scientific paper

We show that the adjunction counit of a Fourier-Mukai transform $\Phi$ from $D(X_1)$ to $D(X_2)$ arises from a map of the kernels of the corresponding Fourier-Mukai transforms in a very general setting of $X_{1,2}$ being proper separable schemes of finite type over a field. We write down this map of kernels explicitly - facilitating the computation of the twist (the cone of the adjunction counit) of $\Phi$. We also give another description of this map, better suited to computing cones in the case when the kernel of $\Phi$ is a pushforward from a subscheme $D$ of $X_1 \times X_2$. Moreoever, we show that we can replace the condition of properness of the spaces $X_{1,2}$ by that of $D$ being proper over $X_{1,2}$ and still have this description apply as-is. This can be used, for instance, to compute spherical twists on non-proper varieties directly and in full generality.

Affiliated with

Also associated with

No associations

Rating

On taking twists of Fourier-Mukai transforms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On taking twists of Fourier-Mukai transforms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On taking twists of Fourier-Mukai transforms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-377690