Geodesic
The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines
Documenta mathematica, Tome 27 (2022), pp. 869-916 Cet article a éte moissonné depuis la source EMS Press

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Given a central arrangement of lines A in a 2-dimensional vector space V over a field of characteristic zero, we study the algebra D(A) of differential operators on V which are logarithmic along A. Among other things we determine the Hochschild cohomology of D(A) as a Gerstenhaber algebra, establish a connection between that cohomology and the de Rham cohomology of the complement M(A) of the arrangement, determine the isomorphism group of D(A) and classify the algebras of that form up to isomorphism.
DOI : 10.4171/dm/887
Classification : 14N20, 16E40
Mots-clés : hyperplane arrangements, algebra of differential operators, Hoshchild cohomology 
@article{10_4171_dm_887,
     author = {Francisco Kordon and Mariano Su\'arez-\'Alvarez},
     title = {The {Hochschild} cohomology of the algebra of differential operators tangent to a central arrangement of lines},
     journal = {Documenta mathematica},
     pages = {869--916},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/887},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/887/}
}
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Francisco Kordon; Mariano Suárez-Álvarez. The Hochschild cohomology of the algebra of differential operators tangent to a central arrangement of lines. Documenta mathematica, Tome 27 (2022), pp. 869-916. doi: 10.4171/dm/887

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