6533b85bfe1ef96bd12ba246

RESEARCH PRODUCT

Symmetries and equations of smooth quartic surfaces with many lines

Davide Cesare Veniani

subject

Fermat's Last TheoremPure mathematicsGeneral Mathematics010102 general mathematics14J28 14N25Automorphism01 natural sciencesK3 surfaceMathematics - Algebraic GeometryMathematics::Algebraic GeometryQuartic functionLine (geometry)Homogeneous spaceFOS: Mathematics0101 mathematicsQuartic surfaceAlgebraic Geometry (math.AG)Mathematics

description

We provide explicit equations of some smooth complex quartic surfaces with many lines, including all 10 quartics with more than 52 lines. We study the relation between linear automorphisms and some configurations of lines such as twin lines and special lines. We answer a question by Oguiso on a determinantal presentation of the Fermat quartic surface.

https://doi.org/10.4171/rmi/1127