2011
http://publications.mfo.de/handle/mfo/1343
Mon, 04 Mar 2024 18:54:59 GMT2024-03-04T18:54:59ZSecond Main Theorems and Unicity of Meromorphic Mappings with Moving Hypersurfaces
http://publications.mfo.de/handle/mfo/1250
Second Main Theorems and Unicity of Meromorphic Mappings with Moving Hypersurfaces
Si, Duc Quang
In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove a uniqueness theorem for these mappings sharing few moving hypersurfaces without counting multiplicity. This result is an improvement of the results of Dulock - Min Ru [2] and Dethloff - Tan [4]. Moreover the meromorphic mappings maybe algebraically degenerate.
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12502011-01-01T00:00:00ZSi, Duc QuangIn this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove a uniqueness theorem for these mappings sharing few moving hypersurfaces without counting multiplicity. This result is an improvement of the results of Dulock - Min Ru [2] and Dethloff - Tan [4]. Moreover the meromorphic mappings maybe algebraically degenerate.The Cleavage Operad and String Topology of Higher Dimension
http://publications.mfo.de/handle/mfo/1249
The Cleavage Operad and String Topology of Higher Dimension
Bargheer, Tarje
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12492011-01-01T00:00:00ZBargheer, TarjeThe T-Graph of a Multigraded Hilbert Scheme
http://publications.mfo.de/handle/mfo/1248
The T-Graph of a Multigraded Hilbert Scheme
Hering, Milena; Maclagan, Diane
The $T$-graph of a multigraded Hilbert scheme records the zero and one-dimensional orbits of the $T=(K^*)^n$ action on the Hilbert scheme induced from the $T$-action on $\mathbb{A}^n$. It has vertices the $T$-fixed points, and edges the onedimensional $T$-orbits. We give a combinatorial necessary condition for the existence of an edge between two vertices in this graph. For the Hilbert scheme of points in the plane, we give an explicit combinatorial description of the equations defining the scheme parameterizing all one-dimensional torus orbits whose closures contain two given monomial ideals. For this Hilbert scheme we show that the $T$-graph depends on the ground field, resolving a question of Altmann and Sturmfels.
OWLF 2010
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12482011-01-01T00:00:00ZHering, MilenaMaclagan, DianeThe $T$-graph of a multigraded Hilbert scheme records the zero and one-dimensional orbits of the $T=(K^*)^n$ action on the Hilbert scheme induced from the $T$-action on $\mathbb{A}^n$. It has vertices the $T$-fixed points, and edges the onedimensional $T$-orbits. We give a combinatorial necessary condition for the existence of an edge between two vertices in this graph. For the Hilbert scheme of points in the plane, we give an explicit combinatorial description of the equations defining the scheme parameterizing all one-dimensional torus orbits whose closures contain two given monomial ideals. For this Hilbert scheme we show that the $T$-graph depends on the ground field, resolving a question of Altmann and Sturmfels.Analytic Varieties with Finite Volume Amoebas are Algebraic
http://publications.mfo.de/handle/mfo/1247
Analytic Varieties with Finite Volume Amoebas are Algebraic
Madani, Farid; Nisse, Mounir
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 is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the $k$-linear spaces will be given.
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12472011-01-01T00:00:00ZMadani, FaridNisse, MounirIn 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 is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the $k$-linear spaces will be given.Products of pairs of Dehn twists and maximal real Lefschetz fibrations
http://publications.mfo.de/handle/mfo/1246
Products of pairs of Dehn twists and maximal real Lefschetz fibrations
Degtyarev, Alex; Salepci, Nermin
We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz bration is algebraic.
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12462011-01-01T00:00:00ZDegtyarev, AlexSalepci, NerminWe address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz bration is algebraic.Positive recurrence of piecewise Orntein-Uhlenbeck processes and common quadratic Lyapunov functions
http://publications.mfo.de/handle/mfo/1245
Positive recurrence of piecewise Orntein-Uhlenbeck processes and common quadratic Lyapunov functions
Dieker, A. B.; Gao, Xuefeng
We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to `overload' and `underload'. The two regimes cause standard techniques for proving positive recurrence to fail. Using and extending the framework of common quadratic Lyapunov functions from the theory of control, we construct Lyapunov functions for the diffusion approximations corresponding to systems with and without abandonment. With these Lyapunov functions, we prove that piecewise OU processes have a unique stationary distribution.
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12452011-01-01T00:00:00ZDieker, A. B.Gao, XuefengWe study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to `overload' and `underload'. The two regimes cause standard techniques for proving positive recurrence to fail. Using and extending the framework of common quadratic Lyapunov functions from the theory of control, we construct Lyapunov functions for the diffusion approximations corresponding to systems with and without abandonment. With these Lyapunov functions, we prove that piecewise OU processes have a unique stationary distribution.Upper bounds for the number of solutions to quartic thue equations
http://publications.mfo.de/handle/mfo/1244
Upper bounds for the number of solutions to quartic thue equations
Akhtari, Shabnam
We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve $\phi(x,y)$ that allows us to use the theory of linear forms in logarithms. This manuscript improves the results of author's earlier work with Okazaki [2] by giving special treatments to forms with respect to their signature.
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12442011-01-01T00:00:00ZAkhtari, ShabnamWe will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve $\phi(x,y)$ that allows us to use the theory of linear forms in logarithms. This manuscript improves the results of author's earlier work with Okazaki [2] by giving special treatments to forms with respect to their signature.New representations of matroids and generalizations
http://publications.mfo.de/handle/mfo/1243
New representations of matroids and generalizations
Izhakian, Zur; Rhodes, John L.
We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This idea of representations is naturally generalized to include hereditary collections (also known as abstract simplicial complexes). We show that a matroid that can be directly decomposed as matroids, each of which is representable over a field, has a boolean representation, and more generally that any arbitrary hereditary collection is superboolean-representable.
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12432011-01-01T00:00:00ZIzhakian, ZurRhodes, John L.We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This idea of representations is naturally generalized to include hereditary collections (also known as abstract simplicial complexes). We show that a matroid that can be directly decomposed as matroids, each of which is representable over a field, has a boolean representation, and more generally that any arbitrary hereditary collection is superboolean-representable.Monoid valuations and value ordered supervaluations
http://publications.mfo.de/handle/mfo/1242
Monoid valuations and value ordered supervaluations
Izhakian, Zur; Knebusch, Manfred; Rowen, Louis
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 discussed have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. Basics of a theory of such semirings and transmissions are developed as far as needed.
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12422011-01-01T00:00:00ZIzhakian, ZurKnebusch, ManfredRowen, LouisWe 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 discussed have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. Basics of a theory of such semirings and transmissions are developed as far as needed.Classification of totally real elliptic Lefschetz fibrations via necklace diagrams
http://publications.mfo.de/handle/mfo/1241
Classification of totally real elliptic Lefschetz fibrations via necklace diagrams
Salepci, Nermin
We show that totally real elliptic Lefschetz brations that admit a real section are classified by their "real loci" which is nothing but an $S^1$-valued Morse function on the real part of the total space. We assign to each such real locus a certain combinatorial object that we call a $necklace diagram$. On the one hand, each necklace diagram corresponds to an isomorphism class of a totally real elliptic Lefschetz fibration that admits a real section, and on the other hand, it refers to a decomposition of the identity into a product of certain matrices in $PSL(2,Z)$. Using an algorithm to find such decompositions, we obtain an explicit list of necklace diagrams associated with certain classes of totally real elliptic Lefschetz fibrations. Moreover, we introduce refinements of necklace diagrams and show that refined necklace diagrams determine uniquely the isomorphism classes of the totally real elliptic Lefschetz fibrations which may not have a real section. By means of necklace diagrams we observe some interesting phenomena underlying special feature of real fibrations.
OWLF 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://publications.mfo.de/handle/mfo/12412011-01-01T00:00:00ZSalepci, NerminWe show that totally real elliptic Lefschetz brations that admit a real section are classified by their "real loci" which is nothing but an $S^1$-valued Morse function on the real part of the total space. We assign to each such real locus a certain combinatorial object that we call a $necklace diagram$. On the one hand, each necklace diagram corresponds to an isomorphism class of a totally real elliptic Lefschetz fibration that admits a real section, and on the other hand, it refers to a decomposition of the identity into a product of certain matrices in $PSL(2,Z)$. Using an algorithm to find such decompositions, we obtain an explicit list of necklace diagrams associated with certain classes of totally real elliptic Lefschetz fibrations. Moreover, we introduce refinements of necklace diagrams and show that refined necklace diagrams determine uniquely the isomorphism classes of the totally real elliptic Lefschetz fibrations which may not have a real section. By means of necklace diagrams we observe some interesting phenomena underlying special feature of real fibrations.