Bounds for smooth Fano weighted complete intersections

Abstract

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.

31 pages

References in corpus (4)

• Effective non-vanishing for Fano weighted complete intersections
• Katzarkov-Kontsevich-Pantev Conjecture for Fano threefolds
• Birationally rigid Fano cyclic covers
• Explicit rationality of some cubic fourfolds

Cited by in corpus (12)

• Effective non-vanishing for Fano weighted complete intersections
• Automorphisms of weighted complete intersections
• Nef partitions for codimension 2 weighted complete intersections
• On smooth Fano fourfolds of Picard number two
• Smooth Fano four folds in Gorenstein formats
• The classification of smooth well-formed Fano weighted complete intersections
• Smooth weighted hypersurfaces that are not stably rational
• On K-stability of Fano weighted hypersurfaces
• On smooth Calabi-Yau threefolds of Picard number two
• Weighted Grassmannians and their explicit description
• Belyi's theorem for smooth complete intersections of general type in generalised Grassmannians and weighted projective spaces
• 1-Cycles on Fano varieties