Towards the Classification of Weak Fano Threefolds with ρ= 2

Details Towards the Classification of Weak Fano Threefolds with ρ= 2 Towards the Classification of Weak Fano Threefolds with ρ= 2

2010-09-25

arxiv.org/abs/1009.5036v2

Mathematics

Algebraic Geometry

35 pages, updated 12/28/2011

Scientific paper

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.

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