| Résume||zoom 396 751 8661, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han.
Abstract: If X is a threefold with a nonfactorial ordinary double point, we show that
there is a semiorthogonal decomposition of the derived category of X with two components,
a "small" component responsible for the singularity (we say it "absorbs" the singularity
of the derived category of X), and a "big" component that deforms to the derived category
of a smoothing of X. We use this construction to relate the derived categories of Fano
threefolds of index 2 and degree d to derived categories of Fano threefolds of index 1
and genus g = 2d + 2. This is joint work in progress with Evgeny Shinder.|