Bounds for smooth Fano weighted complete intersections
Victor Przyjalkowski, Constantin Shramov
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.
Topics & Concepts
Fano planeMathematicsComplete intersectionProjective spaceIntersection (aeronautics)Dimension (graph theory)CombinatoricsClass (philosophy)Projective testSpace (punctuation)Pure mathematicsUpper and lower boundsCone (formal languages)Discrete mathematicsProjective varietyMathematical analysisComputer scienceAlgorithmArtificial intelligenceOperating systemAerospace engineeringEngineeringAlgebraic Geometry and Number TheoryPolynomial and algebraic computationCommutative Algebra and Its Applications