Przyjalkowski, Victor; Shramov, Constantin Bounds for smooth Fano weighted complete intersections. (English) Zbl 1452.14043 Commun. Number Theory Phys. 14, No. 3, 511-553 (2020). Whereas the classification of smooth Fano varieties is achieved in dimension up to 3, there is no systematic approach to tackle the situation in which the dimension is greater than 3. In the paper under review, the authors examine the case of smooth Fano complete intersections \(X\) in weighted projective spaces. When \(X\) is well-formed and is not an intersection with linear cones, sharp bounds on the weights of the corresponding ambient weighted projective spaces are obtained.As a consequence of these bounds, the authors give a classification of smooth well-formed Fano weighted complete intersections of dimension 4 and 5. In addition, they deduce their Hodge numbers, together with the degrees of their defining equations, their anticanonical degrees \(K^4\) and \(K^5\) respectively, and the dimension \(h^0(-K)\) (content of Tables 1 and 3). Reviewer: Livia Campo (Nottingham) Cited in 8 Documents MSC: 14J45 Fano varieties 14M10 Complete intersections Keywords:weighted complete intersections; Fano varieties; bounds; Lagrange multipliers PDFBibTeX XMLCite \textit{V. Przyjalkowski} and \textit{C. Shramov}, Commun. Number Theory Phys. 14, No. 3, 511--553 (2020; Zbl 1452.14043) Full Text: DOI arXiv