Now showing items 1-20 of 41

• #### Abundance of 3-Planes on Real Projective Hypersurfaces ﻿

[OWP-2014-14] (Mathematisches Forschungsinstitut Oberwolfach, 2014-11-11)
We show that a generic real projective n-dimensional hypersurface of odd degree $d$, such that $4(n-2)=\binom{d+3}{3}$, contains "many" real 3-planes, namely, in the logarithmic scale their number has the same rate of ...
• #### Affine Space Fibrations ﻿

[OWP-2018-19] (Mathematisches Forschungsinstitut Oberwolfach, 2018-09-05)
We discuss various aspects of affine space fibrations. Our interest will be focused in the singular fibers, the generic fiber and the propagation of properties of a given smooth special fiber to nearby fibers.
• #### Analytic Varieties with Finite Volume Amoebas are Algebraic ﻿

[OWP-2011-33] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
In this paper, we study the amoeba volume of a given $k$-dimensional generic analytic variety $V$ of the complex algebraic torus $(C^*)^n$. When $n>=2k$, we show that $V$ is algebraic if and only if the volume of its amoeba ...
• #### Cocharacter-closure and spherical buildings ﻿

[OWP-2015-12] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)
Let $k$ be a field, let $G$ be a reductive $k$-group and $V$ an affine $k$-variety on which $G$ acts. In this note we continue our study of the notion of cocharacter-closed $G(k)$-orbits in $V$. In earlier work we used a ...
• #### Cocharacter-Closure and the Rational Hilbert-Mumford Theorem ﻿

[OWP-2014-16] (Mathematisches Forschungsinstitut Oberwolfach, 2014-12-20)
For a field $k$, let $G$ be a reductive $k$-group and $V$ an affine $k$-variety on which $G$ acts. Using the notion of cocharacter-closed $G(k)$-orbits in $V$ , we prove a rational version of the celebrated Hilbert-Mumford ...
• #### Criteria for Algebraicity of Analytic Functions ﻿

[OWP-2018-25] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-12)
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 ...
• #### Cryptanalysis of Public-key Cryptosystems Based on Algebraic Geometry Codes ﻿

[OWP-2012-01] (Mathematisches Forschungsinstitut Oberwolfach, 2012-03-20)
This paper addresses the question of retrieving the triple $(\mathcal{X},\mathcal{P},\mathcal{E})$ from the algebraic geometry code $\mathcal{C}_L(\mathcal{X},\mathcal{P},\mathcal{E})$, where $\mathcal{X}$ is an algebraic ...
• #### Deformation Classification of Real Non-Singular Cubic Threefolds with a Marked Line ﻿

[OWP-2018-02] (Mathematisches Forschungsinstitut Oberwolfach, 2018-02-21)
We prove that the space of pairs $(X,l)$ formed by a real non-singular cubic hypersurface $X\subset P^4$ with a real line $l\subset X$ has 18 connected components and give for them several quite explicit interpretations. ...
• #### Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps ﻿

[OWP-2018-20] (Mathematisches Forschungsinstitut Oberwolfach, 2018-10-08)
Demailly's conjecture, which is a consequence of the Green-Griffiths-Lang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to ...
• #### Dominance and Transmissions in Supertropical Valuation Theory ﻿

[OWP-2011-07] (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 ...
• #### 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 ...
• #### Global Variants of Hartogs' Theorem ﻿

[OWP-2018-24] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-06)
Hartogs' theorem asserts that a separately holomorphic function, defined on an open subset of $\mathbb{C}^n$, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open ...
• #### 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 ...
• #### Infeasibility certificates for linear matrix inequalities ﻿

[OWP-2011-28] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-25)
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 ...
• #### The Magic Square of Reflections and Rotations ﻿

[OWP-2018-13] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-01)
We show how Coxeter’s work implies a bijection between complex reflection groups of rank two and real reflection groups in 0(3). We also consider this magic square of reflections and rotations in the framework of Clifford ...
• #### A McKay Correspondence for Reflection Groups ﻿

[OWP-2018-14] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-02)
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 $\mathbb P^3$ ﻿

[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 ...
• #### Monoid valuations and value ordered supervaluations ﻿

[OWP-2011-17] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations ...