| Abstrakt: |
Building on the work of Mukai, we explore the birational geometry of the moduli spaces M S , L of semistable rank two torsion-free sheaves, with c 1 = - K S and c 2 = 2 , on a polarized degree one del Pezzo surface (S, L); this is related to the birational geometry of the blow-up X of P 4 in 8 points. Our analysis is explicit and is obtained by looking at the variation of stability conditions. Then we provide a careful investigation of the blow-up X and of the moduli space Y = M S , - K S , which is a remarkable family of smooth Fano fourfolds. In particular we describe the relevant cones of divisors of Y, the group of automorphisms, and the base loci of the anticanonical and bianticanonical linear systems. [ABSTRACT FROM AUTHOR] |
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