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Combinatorics and topology of toric arrangements defined by root systems
- Publication Year :
- 2008
-
Abstract
- Given the toric (or toral) arrangement defined by a root system $\Phi$, we describe the poset of its layers (connected components of intersections) and we count its elements. Indeed we show how to reduce to zero-dimensional layers, and in this case we provide an explicit formula involving the maximal subdiagrams of the affine Dynkin diagram of $\Phi$. Then we compute the Euler characteristic and the Poincare' polynomial of the complement of the arrangement, which is the set of regular points of the torus.<br />Comment: 20 pages. Updated version of a paper published in December 2008
- Subjects :
- Connected component
Polynomial
General Mathematics
Torus
Combinatorics
symbols.namesake
Dynkin diagram
Euler characteristic
symbols
FOS: Mathematics
Algebraic Topology (math.AT)
Mathematics - Combinatorics
Affine transformation
Combinatorics (math.CO)
Mathematics - Algebraic Topology
14N10, 17B10, 20G20
Representation Theory (math.RT)
Partially ordered set
Mathematics - Representation Theory
Mathematics
Complement (set theory)
Subjects
Details
- Language :
- Italian
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....a4eb3baa9600b21588eb868464179600