Towards the Classification of Weak Fano Threefolds with ρ= 2

Abstract

In this paper, we provide examples of Sarkisov links of type II between complex projective Fano threefolds $X$ with $\rho (X)=1$. To show examples of these links, we study smooth weak Fano threefolds with extremal rays of type $E$. We further assume that the pluri-anticanonical morphism contracts only a finite number of curves. We numerically classify smooth weak Fano threefolds with $\rho (X)=2$ having an extremal ray of type $E$ both before and after a flop as well as prove the existence of some of these numerical cases.

arXiv comment36 pages, updated 1/6/2014