Zhixin Xie (Saarbrücken): Anticanonical geometry of the blow-up of P^4 in 8 points and its Fano model
001
batiment I
Mukai realised the blow-up X of P^4 in 8 points as a moduli
space of vector bundles on a degree-one del Pezzo surface. With the same
construction, Casagrande-Codogni-Fanelli associated to the degree-one
del Pezzo surface S a smooth Fano fourfold Y with remarkable geometric
properties, and described explicitly the interplay between S, X and Y.
Building on their work, we continue to explore the birational geometry
of Y which is an important example of Fano fourfold. We will describe
completely the base scheme of the anticanonical system of Y, and discuss
the action of the Bertini involution on Y induced by the Bertini
involution on S. In particular, we will explain the relation between the
Bertini involution and the anticanonical map of Y, and show that the
involution preserves every divisor in the anticanonical system of Y.