Abstract

The Gale correspondence provides a duality between sets of n general points inprojective spaces Ps and Pr when n equals r s 2. By a result of Mukai, the blow-up of P4at 8 points say X, can be realized as a moduli space of torsion-free rank 2 semi-stable sheaves(with certain fixed Chern class datum) on the blow-up of P2 in 8 Gale dual points. In a recentwork, Casagrande, Codogni and Fanelli use this to describe the Mori chamber decomposition ofthe effective cone of divisors of X. It was shown by Castravet and Tevelev that the blow-up ofPr at n points for the case when r ≥ 5 and n ≥ r + 4 is no longer a Mori dream space. In jointwork with Carolina Araujo, Ana-Maria Castravet and Diletta Martinelli we show that even inthis case it is possible to give a Mori chamber type decomposition for a part of the effectivecone.1