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Exceptional collections, and the Néron–Severi lattice for surfaces
(ElsevierAdvances in Mathematics, 2017-01-10)
We work out properties of smooth projective varieties X over a (not necessarily algebraically closed) field $\textit{k}$ that admit collections of objects in the bounded derived category of coherent sheaves D$^{b}$(X) that ...
On the motive of some hyperKaehler varieties
(De GruyterJournal für die reine und angewandte Mathematik, 2015-06-05)
We show that the motive of the Hilbert scheme of length-n subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, ...
The Fourier transform for certain hyperKähler fourfolds
(American Mathematical SocietyThe Fourier transform for certain hyperKähler fourfolds, 2015-11-18)
Using a codimension-1 algebraic cycle obtained from the Poincar e line bundle, Beauville de ned the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition ...