Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 07/2017, Volume 163, Issue 1, pp. 161 - 172

... 2016 161 Freeness versus maximal global Tjurina number for plane curves BY ALEXANDRU DIMCA Université Côte d’Azur, CNRS, LJAD, France. e-mail: dimca@unice.fr...

MATHEMATICS | Curves (geometry)

MATHEMATICS | Curves (geometry)

Journal Article

1992, Universitext., ISBN 9780387977096, xvi, 263

Book

Journal of algebraic combinatorics, ISSN 1572-9192, 2018, Volume 50, Issue 4, pp. 363 - 378

... Alexandru Dimca 1 · Gabriel Sticlaru 2 Received: 16 December 2017 / Accepted: 9 November 2018 / Published online: 8 December 2018 © Springer Science+Business Media, LLC...

Terao’s conjecture | Tjurina number | Slope Problem | Mathematics | Jacobian syzygy | Free line arrangement | Primary 14H50 | 13D02 | Secondary 14B05 | 32S22 | Nearly free line arrangement | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Algebraic Geometry

Terao’s conjecture | Tjurina number | Slope Problem | Mathematics | Jacobian syzygy | Free line arrangement | Primary 14H50 | 13D02 | Secondary 14B05 | 32S22 | Nearly free line arrangement | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Algebraic Geometry

Journal Article

1987, ISBN 3528089997, xvii, 242

Book

Documenta Mathematica, ISSN 1431-0643, 2018, Volume 23, pp. 1 - 14

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 07/2018, Volume 29, Issue 8, p. 1850055

We give a formula relating the total Tjurina number and the generic splitting type of the bundle of logarithmic vector fields associated to a reduced plane...

splitting type | Milnor and Tjurina numbers | freeness and near freeness | Logarithmic vector fields | plane curves and line arrangements | MATHEMATICS | FREENESS | ARRANGEMENTS

splitting type | Milnor and Tjurina numbers | freeness and near freeness | Logarithmic vector fields | plane curves and line arrangements | MATHEMATICS | FREENESS | ARRANGEMENTS

Journal Article

Collectanea mathematica (Barcelona), ISSN 2038-4815, 2019, Volume 71, Issue 3, pp. 407 - 425

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 12/2019, Volume 223, Issue 12, pp. 5055 - 5066

In this note we describe the minimal resolution of the ideal If, the saturation of the Jacobian ideal of a nearly free plane curve C:f=0. In particular, it...

Tjurina number | Nearly free curve | Rational cuspidal curve | Jacobian ideal | Free curve | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | LEFSCHETZ PROPERTIES | CONFIGURATIONS | Algebraic Geometry | Commutative Algebra | Mathematics

Tjurina number | Nearly free curve | Rational cuspidal curve | Jacobian ideal | Free curve | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | LEFSCHETZ PROPERTIES | CONFIGURATIONS | Algebraic Geometry | Commutative Algebra | Mathematics

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2014, Volume 16, Issue 4, pp. 1350025 - 1-1350025-47

For a space, we investigate its CJL (cohomology jump loci), sitting inside varieties of representations of the fundamental group. To do this, for a CDG...

analytic local ring | quasi-projective manifold | nilmanifold | Artinian ring | arrangement | cohomology support loci | covariant derivative | formal space | Representation variety | flat connection | monodromy | Malcev completion | minimal model | KAHLER-MANIFOLDS | MATHEMATICS, APPLIED | NILPOTENT GROUPS | DEFORMATION-THEORY | HOMOTOPY THEORY | COMPACT KAHLER | LIE-ALGEBRAS | MATHEMATICS | FORMALITY PROPERTIES | FUNDAMENTAL-GROUPS | COEFFICIENTS | Origins | Algebra | Mathematical analysis | Spectra | Representations | Topology | Loci | Joints

analytic local ring | quasi-projective manifold | nilmanifold | Artinian ring | arrangement | cohomology support loci | covariant derivative | formal space | Representation variety | flat connection | monodromy | Malcev completion | minimal model | KAHLER-MANIFOLDS | MATHEMATICS, APPLIED | NILPOTENT GROUPS | DEFORMATION-THEORY | HOMOTOPY THEORY | COMPACT KAHLER | LIE-ALGEBRAS | MATHEMATICS | FORMALITY PROPERTIES | FUNDAMENTAL-GROUPS | COEFFICIENTS | Origins | Algebra | Mathematical analysis | Spectra | Representations | Topology | Loci | Joints

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 03/2019, Volume 91, pp. 98 - 115

We describe an algorithm computing the monodromy and the pole order filtration on the Milnor fiber cohomology of any reduced projective plane curve C. The...

Pole order filtration | Milnor fiber | b-Function | Plane curve | Monodromy | POLYNOMIALS | MATHEMATICS, APPLIED | FIBRATIONS | COMPUTER SCIENCE, THEORY & METHODS | SPECTRUM | IDEALS | Algorithms | Mathematics

Pole order filtration | Milnor fiber | b-Function | Plane curve | Monodromy | POLYNOMIALS | MATHEMATICS, APPLIED | FIBRATIONS | COMPUTER SCIENCE, THEORY & METHODS | SPECTRUM | IDEALS | Algorithms | Mathematics

Journal Article

Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2018, Volume 54, Issue 1, pp. 163 - 179

We define a class of plane curves that are close to the free divisors in terms of the local cohomology of their Jacobian algebras and such that, conjecturally,...

Rational cuspidal curve | Jacobian ideal | Milnor algebra | Free divisor | MATHEMATICS | LINE ARRANGEMENTS | rational cuspidal curve

Rational cuspidal curve | Jacobian ideal | Milnor algebra | Free divisor | MATHEMATICS | LINE ARRANGEMENTS | rational cuspidal curve

Journal Article

Nagoya mathematical journal, ISSN 0027-7630, 06/2012, Volume 206, pp. 75 - 97

The order of the Milnor fiber monodromy operator of a central hyperplane arrangement is shown to be combinatorially determined. In particular, a necessary and...

COMPLEMENTS | MATHEMATICS | EIGENVALUES | COHOMOLOGY | MILNOR FIBERS | 32S35 | 32S25 | 32S22 | 32S55

COMPLEMENTS | MATHEMATICS | EIGENVALUES | COHOMOLOGY | MILNOR FIBERS | 32S35 | 32S25 | 32S22 | 32S55

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2016, Volume 18, Issue 4, p. 1550065

We show that the fundamental groups of normal complex algebraic varieties share many properties of the fundamental groups of smooth varieties. The jump loci of...

Twisted cohomology | Local system | Normal variety | Characteristic variety | Fundamental group | TOPOLOGY | MATHEMATICS, APPLIED | fundamental group | INVARIANTS | PRESENTATIONS | COHOMOLOGY JUMP LOCI | MATHEMATICS | twisted cohomology | characteristic variety | local system | PROJECTIVE VARIETIES | SETS | SYSTEMS | GEOMETRY | Algebraic Geometry | Mathematics

Twisted cohomology | Local system | Normal variety | Characteristic variety | Fundamental group | TOPOLOGY | MATHEMATICS, APPLIED | fundamental group | INVARIANTS | PRESENTATIONS | COHOMOLOGY JUMP LOCI | MATHEMATICS | twisted cohomology | characteristic variety | local system | PROJECTIVE VARIETIES | SETS | SYSTEMS | GEOMETRY | Algebraic Geometry | Mathematics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2019, Volume 342, Issue 8, pp. 2445 - 2453

We prove Terao conjecture saying that the freeness is determined by the combinatorics for arrangements of 13 lines in the complex projective plane.

Terao’s conjecture | Intersection lattice | Line arrangement | Free arrangement | MATHEMATICS | EXPONENTS | Terao's conjecture | HYPERPLANES

Terao’s conjecture | Intersection lattice | Line arrangement | Free arrangement | MATHEMATICS | EXPONENTS | Terao's conjecture | HYPERPLANES

Journal Article

2017, Universitext, ISBN 3319562207

This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of...

Commutative algebra | Functions of complex variables | Algorithms | Mathematics | Combinatorics | Algebraic geometry | Commutative rings | Projective geometry

Commutative algebra | Functions of complex variables | Algorithms | Mathematics | Combinatorics | Algebraic geometry | Commutative rings | Projective geometry

Web Resource

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2019, Volume 94, Issue 4, p. 689

Journal Article

Compositio mathematica, ISSN 0010-437X, 03/2014, Volume 150, Issue 3, pp. 344 - 368

...COMPOSITIO MATHEMATICA Number of Jordan blocks of the maximal size for local monodromies Alexandru Dimca and Morihiko Saito Compositio Math. 150 (2014), 344...

nearby cycles | limit mixed Hodge structure | local monodromy | HODGE-MODULES | MATHEMATICS | MU-CONSTANT STRATUM | VANISHING CYCLES | THEOREM | HYPERSURFACE SINGULARITIES | Combinatorics | Theorems | Algebra | Singularities | Mathematical analysis | Degeneration | Spectra | Combinatorial analysis | Fibers | Mathematics - Algebraic Geometry | Algebraic Geometry | Mathematics

nearby cycles | limit mixed Hodge structure | local monodromy | HODGE-MODULES | MATHEMATICS | MU-CONSTANT STRATUM | VANISHING CYCLES | THEOREM | HYPERSURFACE SINGULARITIES | Combinatorics | Theorems | Algebra | Singularities | Mathematical analysis | Degeneration | Spectra | Combinatorial analysis | Fibers | Mathematics - Algebraic Geometry | Algebraic Geometry | Mathematics

Journal Article

European journal of mathematics, ISSN 2199-6768, 2019

We show that a general lower bound for the global Tjurina number of a reduced complex projective plane curve, given by A. A. du Plessis and C.T.C. Wall, can be...

Mathematics

Mathematics

Journal Article

Journal of Singularities, ISSN 1949-2006, 2018, Volume 18, pp. 114 - 118

Journal Article

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