On the Picard number of almost Fano threefolds with pseudo-index >1

Details On the Picard number of almost Fano threefolds with pseudo-index >1 On the Picard number of almost Fano threefolds with pseudo-index >1

2006-03-03

arxiv.org/abs/math/0603090v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

We study Gorenstein almost Fano threefolds X with canonical singularities and
pseudoindex > 1. We show that the maximal Picard number of X is 10 in general,
3 if X is Fano, and 8 if X is toric. Moreover, we characterize the boundary
cases. In the Fano case, we prove that the generalized Mukai conjecture holds.

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