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On a generalization of Solomon-Terao formula for subspace arrangements.
- Source :
-
Journal of Algebra . Oct2020, Vol. 560, p266-295. 30p. - Publication Year :
- 2020
-
Abstract
- We investigate in this paper a generalization of Solomon-Terao formula for central equidimensional subspace arrangements. We introduce generalized Solomon-Terao functions based on the Hilbert-Poincaré series of the modules of multi-logarithmic forms and logarithmic multi-residues. We show that as in the case of hyperplane arrangements, these Solomon-Terao functions are polynomial. We then prove that if the Solomon-Terao polynomial of the modules of multi-residues satisfies a certain property, then this polynomial is related to the characteristic polynomial of the subspace arrangement. In particular, we prove that this generalized Solomon-Terao formula holds for any line arrangement of any codimension. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GENERALIZATION
*DIFFERENTIAL forms
*POLYNOMIALS
*HYPERPLANES
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 560
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 144935579
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2020.05.011