Browsing 1  Oberwolfach Preprints (OWP) by MSC "13"
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Abstract Bivariant Cuntz Semigroups
[OWP201704] (Mathematisches Forschungsinstitut Oberwolfach, 20170213)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 ... 
The algebra of differential operators for a Gegenbauer weight matrix
[OWP201507] (Mathematisches Forschungsinstitut Oberwolfach, 20150729)In this work we study in detail the algebra of differential operators $\mathcal{D}(W)$ associated with a Gegenbauer matrix weight. We prove that two second order operators generate the algebra, indeed $\mathcal{D}(W)$ is ... 
Cluster structures on simple complex lie groups and the BelavinDrinfeld classification
[OWP201110] (Mathematisches Forschungsinstitut Oberwolfach, 20110512)We study natural cluster structures in the rings of regular functions on simple complex Lie groups and PoissonLie structutures compatible with these cluster structures. According to our main conjecture, each class in the ... 
Criteria for Algebraicity of Analytic Functions
[OWP201825] (Mathematisches Forschungsinstitut Oberwolfach, 20181112)We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend ... 
Dominance and Transmissions in Supertropical Valuation Theory
[OWP201107] (Mathematisches Forschungsinstitut Oberwolfach, 2011)This paper is a sequel of [IKR1], where we defined supervaluations on a commutative ring $R$ and studied a dominance relation $\Phi >= v$ between supervaluations $\varphi$ and $\upsilon$ on $R$, aiming at an enrichment of ... 
Geometry of Free Loci and Factorization of Noncommutative Polynomials
[OWP201723] (Mathematisches Forschungsinstitut Oberwolfach, 20171002)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 ... 
Infeasibility certificates for linear matrix inequalities
[OWP201128] (Mathematisches Forschungsinstitut Oberwolfach, 20110525)Farkas' lemma is a fundamental result from linear programming providing linear certi cates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly ... 
Linear Syzygies, Hyperbolic Coxeter Groups and Regularity
[OWP201715] (Mathematisches Forschungsinstitut Oberwolfach, 20170524)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. ... 
Matchings and Squarefree Powers of Edge Ideals
[OWP201925] (Mathematisches Forschungsinstitut Oberwolfach, 20191111)Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such ... 
A McKay Correspondence for Reflection Groups
[OWP201814] (Mathematisches Forschungsinstitut Oberwolfach, 20180702)We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies ... 
The Minimal Resolution Conjecture on a general quartic surface in $\mathbb P^3$
[OWP201721] (Mathematisches Forschungsinstitut Oberwolfach, 20170727)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 ... 
Monoid valuations and value ordered supervaluations
[OWP201117] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of mvaluations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations ... 
Numerical Invariants and Moduli Spaces for Line Arrangements
[OWP201702] (Mathematisches Forschungsinstitut Oberwolfach, 20170201)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 ... 
On the Gauss Algebra of Toric Algebras
[OWP201807] (Mathematisches Forschungsinstitut Oberwolfach, 20180425)Let $A$ be a $K$subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\mathbb{G}(A)$ of $A$ is generated by monomials of ... 
Positive Margins and Primary Decomposition
[OWP201206] (Mathematisches Forschungsinstitut Oberwolfach, 2012)We study random walks on contingency tables with fixed marginals, corresponding to a (loglinear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with the same marginals that ... 
Some Homological Properties of Borel Type Ideals
[OWP202203] (Mathematisches Forschungsinstitut Oberwolfach, 20220201)We study ideals of Borel type, including $k$Borel ideals and $t$spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated ... 
Supertropical Quadratic Forms I
[OWP201327] (Mathematisches Forschungsinstitut Oberwolfach, 2013)We initiate the theory of a quadratic form q over a semiring $R$. As customary, one can write $q(x+y)=q(x)+q(y)+b(x,y)$, where b is a companion bilinear form. But in contrast to the ringtheoretic case, the companion ... 
Supertropical semirings and supervaluations
[OWP201005] (Mathematisches Forschungsinstitut Oberwolfach, 2010)We interpret a valuation $\upsilon$ on a ring $R$ as a map $\upsilon:R \rightarrow M$ into a so called bipotent semiring $M$ (the usual maxplus setting), and then define a supervaluation $\varphi$ as a suitable map into ... 
Unexpected Properties of the Klein Configuration of 60 Points in $\mathbb{P}^3$
[OWP202019] (Mathematisches Forschungsinstitut Oberwolfach, 20201007)Felix Klein in course of his study of the regular and its symmetries encountered a highly symmetric configuration of 60 points in $\mathbb{P}^3$. This configuration has appeared in various guises, perhaps post notably as ...