• Freeness of Multi-Reflection Arrangements via Primitive Vector Fields 

      [OWP-2017-10] Hoge, Torsten; Mano, Toshiyuki; Röhrle, Gerhard; Stump, Christian (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] Helton, J. William; Klep, Igor; Volčič, Jurij; Helton, J. William (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] Paunescu, Laurentiu; Tibăr, Mihai-Marius (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] Hoge, Torsten; Röhrle, Gerhard (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] Boij, Mats; Migliore, Juan; Miró-Roig, Rosa M.; Nagel, Uwe (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] Dimca, Alexandru; Ibadula, Denis; Măcinic, Daniela Anca (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 ...