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Hokkaido Mathematical Journal, ISSN 0385-4035, 2011, Volume 40, Issue 3, pp. 375 - 392
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2010, Volume 38, Issue 11, pp. 4348 - 4361
Let Q ∈  [x 1 ,..., x n ] = S be a homogeneous polynomial of degree d. The freeness of the logarithmic derivation module, D(Q... 
Logarithmic derivation module | Graded Betti numbers | MATHEMATICS | ARRANGEMENT | FORMULA | Derivation | Algebra | Equivalence | Modules
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2018, Volume 70, Issue 3, pp. 975 - 988
.... We compute the Chern class of the sheaf of logarithmic derivations along D and compare it with the Chern-Schwartz-MacPherson class of the hypersurface complement... 
Jacobian ideal of linear type | Logarithmic derivation | And Phrases. Chern–Schwartz–MacPherson class | MATHEMATICS | MODULE | logarithmic derivation | Chern-Schwartz-MacPherson class | SINGULAR ALGEBRAIC-VARIETIES
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2017, Volume 24, Issue 1, pp. 153 - 172
...) ideals whose logarithmic derivation module is free, in (not necessarily regular) factorial domains essentially of finite type over a field of characteristic zero... 
Derivation | Logarithmic derivation | Free divisor | Zariski-Lipman conjecture | free divisor | MATHEMATICS | logarithmic derivation | DISCRIMINANTS | CONJECTURE
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 330, Issue 1, pp. 251 - 262
We define primitive derivations for Coxeter arrangements which may not be irreducible. Using those derivations, we introduce the primitive filtrations... 
Logarithmic differential 1-forms | Coxeter groups | Hodge filtrations | Coxeter arrangements | Arrangements of hyperplanes | Basic invariants | Primitive derivations | MATHEMATICS | Mechanical engineering
Journal Article
Canadian mathematical bulletin, ISSN 0008-4395, 03/2018, Volume 61, Issue 1, pp. 166 - 173
...) algebraic variety deûned over a field $k$ of characteristic zero, then $X$ is a hypersurface if and only if the module ${{T}_{{{O}_{{{\mathbb{A}}^{n\,/k}}}(X... 
free divisor | MATHEMATICS | FREE DIVISORS | logarithmic derivation | FREE ARRANGEMENT | DISCRIMINANTS | FREENESS | P-2 | hypersurface | logarithmic vector field | HYPERPLANES
Journal Article
Communications in Algebra, ISSN 0092-7872, 07/2019, Volume 47, Issue 7, pp. 2654 - 2666
In this note, we study the logarithmic derivation module of a non-free arrangement... 
Hyperplane arrangements | logarithmic derivations | MATHEMATICS | Derivation | Lower bounds | Addition theorem
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2013, Volume 63, Issue 3, pp. 1177 - 1203
Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y, homological invariants derived from logarithmic... 
Logarithmic | Hyperplane arrangement | Free divisor | Differential form | free divisor | differential form | COMPLEMENT | ARRANGEMENT | logarithmic | POWERS | LINEAR FREE DIVISORS | DERIVATIONS | MATHEMATICS | hyperplane arrangement | MODULE | CURVE | FREE RESOLUTION | HYPERPLANES
Journal Article
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, ISSN 0025-5645, 10/2019, Volume 71, Issue 4, pp. 1027 - 1047
We introduce a new algebra associated with a hyperplane arrangement A, called the Solomon-Terao algebra ST(A, eta), where eta is a homogeneous polynomial. It... 
MATHEMATICS | logarithmic derivation modules | EXPONENTS | complete intersection ring | free arrangements | Solomon-Terao formula | hyperplane arrangements | Artinian ring
Journal Article
Journal of Algebra, ISSN 0021-8693, 01/2018, Volume 493, pp. 20 - 35
...]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements... 
Weyl group | Shi arrangement | Hyperplane arrangement | Catalan arrangement | Logarithmic derivation | Affine Weyl group | Free arrangement
Journal Article
Journal of algebraic combinatorics, ISSN 1572-9192, 2016, Volume 45, Issue 1, pp. 171 - 189
Journal Article
INVENTIONES MATHEMATICAE, ISSN 0020-9910, 03/2017, Volume 207, Issue 3, pp. 1239 - 1287
.... We use this Liouville complex to connect properties of the D-module generated by to homological data of the Jacobian ideal... 
MATHEMATICS | FREE DIVISORS | ZETA-FUNCTIONS | LOGARITHMIC COMPARISON THEOREM | B-FUNCTIONS | COMPLEXES | SINGULARITY | DUALITY | HYPERPLANE ARRANGEMENTS | DIFFERENTIAL-OPERATORS | IDEALS
Journal Article
Collectanea Mathematica, ISSN 0010-0757, 05/2016, Volume 67, Issue 2, pp. 311 - 328
... in commutative Noetherian rings containing the rational numbers. Our approach is through the study of general logarithmic derivation modules, here dubbed tangential... 
Derivation | Differential ideal | Primary decomposition | Logarithmic derivation | CRITERIA | MATHEMATICS | MATHEMATICS, APPLIED | DERIVATIONS
Journal Article
Journal of Algebra, ISSN 0021-8693, 2009, Volume 322, Issue 8, pp. 2839 - 2847
We study structures of derivation modules of Coxeter multiarrangements with quasi-constant multiplicities by using the primitive derivation... 
Hyperplane arrangements | Coxeter arrangements | Logarithmic vector fields | MATHEMATICS | FREE ARRANGEMENT | CONTACT-ORDER FILTRATION | DERIVATIONS
Journal Article
by Abe, T and Suyama, D
JOURNAL OF ALGEBRA, ISSN 0021-8693, 01/2018, Volume 493, pp. 20 - 35
...]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements... 
Weyl group | MATHEMATICS | Shi arrangement | Hyperplane arrangement | Catalan arrangement | Logarithmic derivation | Affine Weyl group | Free arrangement | COXETER ARRANGEMENTS
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2007, Volume 135, Issue 11, pp. 3631 - 3640
Journal Article
Theoretical and mathematical physics, ISSN 1573-9333, 2012, Volume 173, Issue 1, pp. 1329 - 1358
.... Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant Nichols algebra furnishes an equivalence with the triplet W-algebra in the (p, 1... 
fusion | Theoretical, Mathematical and Computational Physics | Yetter-Drinfeld module | Nichols algebra | Applications of Mathematics | logarithmic conformal field theory | Physics | EXTENSIONS | PHYSICS, MULTIDISCIPLINARY | POINTED HOPF-ALGEBRAS | QUANTUM GROUPS | INVARIANTS | MINIMAL MODELS | CLASSIFICATION | PHYSICS, MATHEMATICAL | CONFORMAL FIELD-THEORY | W-ALGEBRA | GROUP-REPRESENTATIONS | CROSSED-MODULES
Journal Article
Journal of High Energy Physics, ISSN 1126-6708, 09/2007, Volume 2007, Issue 9, pp. 085 - 85
Journal Article
10/2018, ISBN 1107187737
This graduate textbook offers a self-contained introduction to the concepts and techniques of logarithmic geometry, a key tool for analyzing compactification... 
eBook
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