On the existence of certain weak Fano threefolds of Picard number two

Details On the existence of certain weak Fano threefolds of Picard number two On the existence of certain weak Fano threefolds of Picard number two

2011-12-12

arxiv.org/abs/1112.2611v1

Mathematics

Algebraic Geometry

Scientific paper

We construct smooth weak Fano threefolds of Picard number two with small anti-canonical map obtained by blowing up certain curves on a smooth quadric in $\mathbb{P}^4$ and on smooth del Pezzo threefolds of degrees 4 and 5. In addition, we give the construction of weak Fano threefolds with small anti-canonical map arising as blow-ups of prime Fano threefolds $X_{10}, X_{16}$ and $X_{18}$ along twisted cubics.

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