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Working paper

Bounds for smooth Fano weighted complete intersections

We prove that if a smooth variety with non-positive canonical class can be embedded into a weighted projective space of dimension~n as a well formed complete intersection and it is not an intersection with a linear cone therein, then the weights of the weighted projective space do not exceed n+1. Based on this bound we classify all smooth Fano complete intersections of dimensions 4 and 5, and compute their invariants.