• Abundance of 3-Planes on Real Projective Hypersurfaces 

      [OWP-2014-14] Finashin, Sergey; Kharlamov, Viatcheslav (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] Gurjar, Rajendra V.; Masuda, Kayo; Miyanishi, Masayoshi (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] Madani, Farid; Nisse, Mounir (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 ...
    • Characterization of Tropical Planar Curves up to Genus Six 

      [OWP-2022-06] Tewari, Ayush Kumar (Mathematisches Forschungsinstitut Oberwolfach, 2022-03-16)
      We provide new forbidden criterion for realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six.
    • Chirality of Real Non-Singular Cubic Fourfolds and Their Pure Deformation Classification 

      [OWP-2019-14] Finashin, Sergey; Kharlamov, Viatcheslav (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-15)
      In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of ...
    • Cocharacter-closure and spherical buildings 

      [OWP-2015-12] Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, Gerhard (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] Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, Gerhard (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] Bochnak, Jacek; Gwoździewicz, Janusz; Kucharz, Wojciech (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] Márquez-Corbella, Irene; Martínez-Moro, Edgar; Pellikaan, Ruud (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] Finashin, Sergey; Kharlamov, Viatcheslav (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] Javanpeykar, Ariyan; Kamenova, Ljudmila (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 ...
    • Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps (Revised Edition) 

      [OWP-2018-20.2] Javanpeykar, Ariyan; Kamenova, Ljudmila (Mathematisches Forschungsinstitut Oberwolfach, 2020-01-23)
      Demailly's conjecture, which is a consequence of the Green-Griffths-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] Izhakian, Zur; Knebusch, Manfred; Rowen, Louis (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] 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 ...
    • Fundamental Theorem of Projective Geometry over Semirings 

      [OWP-2021-09] Tewari, Ayush Kumar (Mathematisches Forschungsinstitut Oberwolfach, 2021-10-11)
      We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail ...
    • 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 ...
    • Global Variants of Hartogs' Theorem 

      [OWP-2018-24] Bochnak, Jacek; Kucharz, Wojciech (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] 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 ...
    • Infeasibility certificates for linear matrix inequalities 

      [OWP-2011-28] Klep, Igor; Schweighofer, Markus (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 ...