Now showing items 1-5 of 5

• #### Abstract Bivariant Cuntz Semigroups ﻿

[OWP-2017-04] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-13)
We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups $S$ and $T$, there is another Cuntz semigroup $((S,T))$ playing the role of morphisms from $S$ to $T$. Applied ...
• #### 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 ...
• #### Linear Syzygies, Hyperbolic Coxeter Groups and Regularity ﻿

[OWP-2017-15] (Mathematisches Forschungsinstitut Oberwolfach, 2017-05-24)
We build a new bridge between geometric group theory and commutative algebra by showing that the virtual cohomological dimension of a Coxeter group is essentially the regularity of the Stanley–Reisner ring of its nerve. ...
• #### 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 ...