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Calculations about multiplicities.

Manuel Abellanas (1982)

Revista Matemática Hispanoamericana

One gives a formula for the calculation of the local intersection multiplicity index of analytic varieties, analogous to the Bézout formula in the case of algebraic varieties in the projective space, in the case of normal crossings. One obtains also a recurrent process for the calculation of the local intersection multiplicity index of plane analytic curves.

Cale Bases in Algebraic Orders

Martine Picavet-L’Hermitte (2003)

Annales mathématiques Blaise Pascal

Let R be a non-maximal order in a finite algebraic number field with integral closure R ¯ . Although R is not a unique factorization domain, we obtain a positive integer N and a family 𝒬 (called a Cale basis) of primary irreducible elements of R such that x N has a unique factorization into elements of 𝒬 for each x ∈ R coprime with the conductor of R . Moreover, this property holds for each nonzero x ∈ R when the natural map Spec ( R ¯ ) → Spec ( R ) is bijective. This last condition is actually equivalent to several properties linked...

Cambrian fans

Nathan Reading, David E. Speyer (2009)

Journal of the European Mathematical Society

For a finite Coxeter group W and a Coxeter element c of W ; the c -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of W . Its maximal cones are naturally indexed by the c -sortable elements of W . The main result of this paper is that the known bijection cl c between c -sortable elements and c -clusters induces a combinatorial isomorphism of fans. In particular, the c -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for W . The rays...

Characterizations of Lambek-Carlitz type

Emil Daniel Schwab (2004)

Archivum Mathematicum

We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The q -analog of the Lambek-Carlitz type characterization of exponential series is also established.

Cluster categories for algebras of global dimension 2 and quivers with potential

Claire Amiot (2009)

Annales de l’institut Fourier

Let k be a field and A a finite-dimensional k -algebra of global dimension ≤ 2 . We construct a triangulated category 𝒞 A associated to A which, if  A is hereditary, is triangle equivalent to the cluster category of A . When 𝒞 A is Hom-finite, we prove that it is 2-CY and endowed with a canonical cluster-tilting object. This new class of categories contains some of the stable categories of modules over a preprojective algebra studied by Geiss-Leclerc-Schröer and by Buan-Iyama-Reiten-Scott. Our results also...

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