Zhixin Xie (Saarbrücken): Anticanonical geometry of the blow-up of P^4 in 8 points and its Fano model

jeudi 7 avr. 2022, 11:00 → 12:00 Europe/Paris

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.