Now showing items 1-6 of 6

• #### Freeness of Multi-Reflection Arrangements via Primitive Vector Fields ﻿

[OWP-2017-10] (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-20)
In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to ...
• #### Geometry of Free Loci and Factorization of Noncommutative Polynomials ﻿

[OWP-2017-23] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-02)
The free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if ...
• #### Gradient Canyons, Concentration of Curvature, and Lipschitz Invariants ﻿

[OWP-2017-35] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-13)
We find new bi-Lipschitz invariants of holomorphic functions of two variables by using the gradient canyons and by combining analytic and geometric viewpoints on the concentration of curvature.
• #### Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements ﻿

[OWP-2017-14] (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-30)
Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger ...
• #### The Minimal Resolution Conjecture on a general quartic surface in $\mathbb P^3$ ﻿

[OWP-2017-21] (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-27)
Mustaţă has given a conjecture for the graded Betti numbers in the minimal free resolution of the ideal of a general set of points on an irreducible projective algebraic variety. For surfaces in $\mathbb P^3$ this conjecture ...
• #### Numerical Invariants and Moduli Spaces for Line Arrangements ﻿

[OWP-2017-02] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-01)
Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane ...