Communications in Number Theory and Physics
Volume 14 (2020)
Bounds for smooth Fano weighted complete intersections
Pages: 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.
weighted complete intersections, Fano varieties, bounds, Lagrange multipliers
2010 Mathematics Subject Classification
The first-named author is supported by Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. No. 14.641.31.0001.
The second-named author is supported by the HSE University Basic Research Program, Russian Academic Excellence Project “5-100”, and by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”.
Received 11 October 2019
Accepted 6 February 2020
Published 13 July 2020