1. CMB 2010 (vol 54 pp. 520)
|Simple Helices on Fano Threefolds|
Building on the work of Nogin, we prove that the braid group $B_4$ acts transitively on full exceptional collections of vector bundles on Fano threefolds with $b_2=1$ and $b_3=0$. Equivalently, this group acts transitively on the set of simple helices (considered up to a shift in the derived category) on such a Fano threefold. We also prove that on threefolds with $b_2=1$ and very ample anticanonical class, every exceptional coherent sheaf is locally free.
2. CMB 2006 (vol 49 pp. 270)
|A Characterization of Products of Projective Spaces |
We give a characterization of products of projective spaces using unsplit covering families of rational curves.
Keywords:Rational curves, Fano varieties