Infinite series of rational moduli components of stable rank two vector bundles on projective space

Géométrie Algébrique

Salle Kampé de Fériet M2
Mardi, 7 Février, 2017 - 14:00 - 15:00

We study the problem of rationality of an ifinite series of components, the so-called Ein components, of the moduli space M(e,n) of rank 2 stable vector bundles with the first Chern class e=0 or -1 and all possible values of the second Chern class n on projective 3-space. The Ein bundles constituting open dense subsets of these components are defined as cohomology bundles of monads whose members are direct sums of line bundles of degrees depending of nonnegative integers a,b,c, where c>a+b. We show that, in the wide range when c>2a+b-e, the Ein components are rational, and in the rest cases they are stably rational. As a consequence, for increasing n the scheme M(e,n) contains an unbounded number of rational components. An explicit construction of rationality of Ein components for c>2a+b-e and, respectively, of their stable rationality in the remaining cases, is given. This is a joint work with A.Kytmanov and S.Tikhomirov.