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## Bounds for smooth Fano weighted complete intersections

Communications in Number Theory and Physics. 2020. Vol. 14. No. 3. P. 511-553.

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.