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Advances in Mathematics, ISSN 0001-8708, 08/2019, Volume 352, pp. 372 - 405
We introduce tautological systems defined by prehomogeneous actions of reductive algebraic groups. If the complement of the open orbit is a linear free divisor... 
Mixed Hodge modules | Tautological systems | Linear free divisors | PERIOD INTEGRALS | POLYNOMIALS | MATHEMATICS | SYMMETRY | DUALITY | HYPERGEOMETRIC SYSTEMS | Differential equations
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2017, Volume 24, Issue 4, pp. 1023 - 1042
A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of... 
Rational cuspidal curve | Jacobian ideal | Milnor algebra | Free divisor | free divisor | MATHEMATICS | OPEN SURFACES | NUMBER | rational cuspidal curve
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2016, Volume 195, Issue 4, pp. 1393 - 1403
On a metric graph, we introduce the notion of a free divisor as a replacement for the notion of a base point-free complete linear system on a curve. By means... 
Graph | 05C99 | Mathematics, general | Mathematics | Clifford index | 14H51 | Free divisor | 14T05 | MATHEMATICS | MATHEMATICS, APPLIED | TROPICAL CURVES | RANK
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 6/2013, Volume 274, Issue 1, pp. 249 - 261
We investigate differential systems occurring in the study of particular non-isolated singularities, the so-called linear free divisors. We obtain a duality... 
Holonomic dual | 32S40 | Spectral numbers | Mathematics, general | Birkhoff problem | 34M35 | Mathematics | Frobenius manifold | Linear free divisors | Brieskorn lattice | MATHEMATICS
Journal Article
Journal of Singularities, ISSN 1949-2006, 2013, Volume 7, pp. 253 - 274
J. Singul. 7 (2013), 253-274 We describe two situations where adding the adjoint divisor to a divisor D with smooth normalization yields a free divisor. Both... 
Versal deformation | Prehomogeneous vector space | Free divisor | Isolated singularity | Adjoint divisor | Stable map | Mathematics - Algebraic Geometry
Journal Article
Journal of Algebra, ISSN 0021-8693, 05/2016, Volume 453, pp. 221 - 248
Journal Article
Topology and its Applications, ISSN 0166-8641, 2012, Volume 159, Issue 2, pp. 437 - 449
Journal Article
Communications in Algebra, ISSN 0092-7872, 01/2019, Volume 47, Issue 1, pp. 424 - 449
Kaplansky Zero Divisor Conjecture states that if G is a torsion-free group and is a field, then the group ring contains no zero divisor and Kaplansky Unit... 
Kaplansky zero divisor conjecture | 16S34 | Group ring | 20C07 | Kaplansky unit conjecture | torsion-free group | MATHEMATICS | PRODUCT | RINGS | SUBSETS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 08/2014, Volume 287, Issue 11-12, pp. 1383 - 1393
In this paper, we study the minimal free resolution of a nondegenerate projective variety X⊂Pr when X is contained in a variety Y of minimal degree as a... 
Primary: 14N05 | 13D02 | Divisor of a rational normal scroll | Minimal free resolution | MATHEMATICS | VARIETIES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2015, Volume 281, pp. 1242 - 1273
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 5/2013, Volume 37, Issue 3, pp. 523 - 543
Journal Article
manuscripta mathematica, ISSN 0025-2611, 11/2018, Volume 157, Issue 3, pp. 361 - 385
Using a general stable vector bundle, we give an embedding $$\alpha _Y$$ αY of the compactified Jacobian $$\bar{J}(Y)$$ J¯(Y) of an integral nodal curve Y into... 
Geometry | Topological Groups, Lie Groups | 14H60 | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | MATHEMATICS | GENERALIZED PARABOLIC BUNDLES | TORSION-FREE SHEAVES | VECTOR-BUNDLES
Journal Article
Turkish Journal of Mathematics, ISSN 1300-0098, 2016, Volume 40, Issue 4, pp. 824 - 831
SLx be the free semilattice on a finite nonempty set X. There exists an undirected graph Gamma(SLx) associated with SLx whose vertices are the proper subsets... 
Hamiltonian graph | Clique number | Finite free semilattice | Zero-divisor graph | Perfect graph | Domination number | MATHEMATICS | zero-divisor graph | domination number | clique number | perfect graph
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2017, Volume 24, Issue 5, pp. 1477 - 1496
Journal Article
Journal of Commutative Algebra, ISSN 1939-0807, 4/2013, Volume 5, Issue 1, pp. 17 - 47
We present several methods to construct or identify families of free divisors such as those annihilated by many Euler vector fields, including binomial free... 
Discriminant | Saito matrix | Euler | Free divisor | Vector field | Binomial | MATHEMATICS | binomial | discriminant | Euler vector field
Journal Article
Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 09/2013, Volume 49, Issue 3, pp. 393 - 412
We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces whose components intersect in a... 
Hilbert-Samuel polynomial | Jacobian ideal | Free divisor | Normal crossing divisor | Logarithmic derivations | free divisor | LIE-ALGEBRAS | MATHEMATICS | normal crossing divisor | logarithmic derivations
Journal Article
Journal of Number Theory, ISSN 0022-314X, 10/2014, Volume 143, pp. 109 - 124
For any positive integer n, let n=q1⋯qs be the prime factorization of n with q1≥⋯≥qs>1. A positive integer n is said to be ordinary if the smallest positive... 
Divisors | Ordinary integers | Extraordinary integers | Square-free integers | MATHEMATICS
Journal Article
Communications in Algebra, ISSN 0092-7872, 02/2018, Volume 46, Issue 2, pp. 887 - 925
Kaplansky's zero divisor conjecture (unit conjecture, respectively) states that for a torsion-free group G and a field , the group ring [G] has no zero... 
zero divisor | zero unit graph | 16S34 | torsion-free group | group ring | Kaplansky's unit conjecture | Divisor graph | 20C07 | Kaplansky's zero divisor conjecture | Kaplansky’s unit conjecture | Kaplansky’s zero divisor conjecture | MATHEMATICS | GROUP-RINGS | CONJECTURE | Torsion | Group theory
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 09/2015, Volume 14, Issue 7
An infinite family of irreducible homogeneous free divisors in K[x, y, z] is constructed. Indeed, we identify sets of monomials X such that the general... 
syzygy | Free divisor | Saito matrix | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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