Fourier–Mukai transforms for Gorenstein schemes

Relative integral functors for singular fibrations and singular partners

“…This theorem also generalises the extension to varieties with Gorenstein singularities given in [16,Thm. 1.22].…”

“…For projective morphisms one has the following result (see [16]): Proposition 2.3. Let f : Z → T be a projective morphism and O(1) a relatively very ample line bundle.…”

“…In the smooth case, our definition is weaker that the usual one given by Bondal and Orlov, and Theorem 3.6 improves the characterization of full faithfulness of Bondal and Orlov. It should be noticed that we give here a slightly different notion of strong simplicity than the one given in [16] for Gorenstein varieties. Since both characterise the full faithfulness of the corresponding integral functors, they are equivalent in the Gorenstein case.…”

“…The study requires the notions of complexes of relative finite projective dimension and of relative finite homological dimension, which are equivalent in the case of projective morphisms as we proved in [16]. Among the results in Section 2 we can mention Proposition 2.10, where we prove that if the integral functor defined by a kernel K…”

“…Following a completely different path, we started in [16] the study of derived categories and fully faithful integral functors for schemes with Gorenstein singularities or fibred in schemes of that kind, and generalised to that situation the characterisation of full faithfulness originally proved by Bondal and Orlov [6] in the smooth case.…”