Abstract configurations in algebraic geometry
By Igor Dolgachev. 2003
49 citations recorded by the source corpus.
An abstract $(v_k,b_r)$-configuration is a pair of finite sets of cardinalities $v$ and $b$ with a relation on the product of the sets such that each element of the first set is related to the same number $k$ of elements from the second set and each element of the second set is related to the same number $r$ of elements in the first set. An example of an abstract configuration is a finite geometry. In this paper we discuss some examples of abstract configurations and, in particular finite geometries, which one encounters in algebraic geometry.
Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/26d571ca9b20c610bebc5cd36fde5904620bb654
How researchers see this paper
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In Discrete Mathematics and Combinatorics
- Laurent Manivel
- Giancarlo Urzúa
- M. Schmidt
- M. Artebani
- Igor Dolgachev
- J. M. Landsberg
- Alberto Elduque
In Electrical and Electronic Engineering
In Geometry and Topology
- Giancarlo Urzúa
- Laurent Manivel
- M. Schmidt
- Igor Dolgachev
- M. Artebani
- Serge Cantat
- D. Huybrechts
- Carlos Simpson
Citations in the corpus
- Arrangements of curves and algebraic surfaces (2007, background): “Classical examples of incidences are the so-called abstract (aα, bβ)-configurations (see for example [24] or [36]).”
- Rank metric codes (2016, background): “Richmond shows that if one chooses six points in general linear position, that is, such that no five of them lie in one hyperplane, from a four-dimensional space (according to [16, 38], Richmond means projective space), then the intersection points of a line through two points and a space through th”
- The Hesse pencil of plane cubic curves (2006, background): “1Not to be confused with another Hesse’s configuration (124, 163), also related to plane cubic curves, see [15].”
- Configurations of lines and models of Lie algebras (2005, background): “Since we have a sixfold ambiguity on the order of the three lines, we recover the classical fact that the cubic surface has exactly 45 tritangent planes.”