n-blocks collections on Fano manifolds and sheaves with regularity −∞

  • Edoardo Ballico Università di Trento
  • Francesco Malaspina Università di Torino
Keywords: m-block collection, Fano manifold, Coherent sheaves on a Fano manifold, Order of regularity


Let X be a smooth Fano manifold equipped with a “ nice ” n-blocks collection in the sense of [3] and F a coherent sheaf on X . Assume that X is Fano and that all blocks are coherent sheaves. Here we prove that F has regularity −∞ in the sense of [3] if Supp(F) is finite, the converse being true under mild assumptions. The corresponding result is also true when X has a geometric collection in the sense of [2].

Author Biographies

Edoardo Ballico, Università di Trento
Dept. of Mathematics
38050 Povo (TN), Italy
Francesco Malaspina, Università di Torino
Università di Torino
via C. Alberto 10
10123 Torino, Italy