A resolution of the Sylvester-Gallai problem of J.-P. Serre

DOI10.1007/BF02187687zbMath0593.51002WikidataQ56454689 ScholiaQ56454689MaRDI QIDQ1076336

Leroy M. Kelly

Publication date: 1986

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/186383

zbMATH Keywords

Sylvester-Gallai configuration

Mathematics Subject Classification ID

Ordered geometries (ordered incidence structures, etc.) (51G05) Incidence structures embeddable into projective geometries (51A45) Configuration theorems in linear incidence geometry (51A20)

Related Items (22)

A computational approach to Milnor fiber cohomology ⋮ On a conjecture of Kelly on (1, 3)-representation of Sylvester-Gallai designs ⋮ A generalized Sylvester–Gallai-type theorem for quadratic polynomials ⋮ Bichromatic and equichromatic lines in \(\mathbb C^2\) and \(\mathbb R^2\) ⋮ A survey of Sylvester's problem and its generalizations ⋮ Logarithmic bundles and line arrangements, an approach via the standard construction ⋮ A Sylvester-Gallai result for concurrent lines in the complex plane ⋮ On the number of ordinary lines determined by sets in complex space ⋮ Spanoids---An Abstraction of Spanning Structures, and a Barrier for LCCs ⋮ On representing Sylvester-Gallai designs ⋮ On a generalization of the Gallai-Sylvester theorem ⋮ A new Sylvester-Gallai configuration representing the 13-point projective plane in \(R^ 4\) ⋮ Fractional Sylvester–Gallai theorems ⋮ Non-representability of finite projective planes by convex sets ⋮ Sylvester-Gallai for arrangements of subspaces ⋮ The Sylvester-Gallai theorem, colourings and algebra ⋮ On the geometry of real or complex supersolvable line arrangements ⋮ A Sylvester-Gallai type theorem for abelian groups ⋮ Spanoids - An Abstraction of Spanning Structures, and a Barrier for LCCs ⋮ Classification theorem for strong triangle blocking arrangements ⋮ SYLVESTER–GALLAI TYPE THEOREMS FOR APPROXIMATE COLLINEARITY ⋮ IMPROVED RANK BOUNDS FOR DESIGN MATRICES AND A NEW PROOF OF KELLY’S THEOREM

Cites Work

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• Semi-stable curves on algebraic surfaces and logarithmic pluricanonical maps
• Recent results in complex differential geometry
• Calabi's conjecture and some new results in algebraic geometry
• The Lines and Planes Connecting the Points of a Finite Set
• On the Chern numbers of surfaces of general type

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