Matrix factorizations for domestic triangle singularities

Dawid Edmund Kędzierski; Helmut Lenzing; Hagen Meltzer

Displaying similar documents to “Matrix factorizations for domestic triangle singularities”

Gorenstein projective complexes with respect to cotorsion pairs

Renyu Zhao, Pengju Ma (2019)

Czechoslovak Mathematical Journal

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Let $(𝒜, ℬ)$ be a complete and hereditary cotorsion pair in the category of left $R$ -modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair $(𝒜, ℬ)$ are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair $(𝒜, ℬ)$ . As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion...

Singularities in Muckenhoupt weighted function spaces

Dorothee D. Haroske (2008)

Banach Center Publications

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We study weighted function spaces of Lebesgue, Besov and Triebel-Lizorkin type where the weight function belongs to some Muckenhoupt $_{p}$ class. The singularities of functions in these spaces are characterised by means of envelope functions.

Projective representations of $S_{n}$ : ring structure and inductive formulae

P. Hoffman (1990)

Banach Center Publications

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Analytic enclosure of the fundamental matrix solution

Roberto Castelli, Jean-Philippe Lessard, Jason D. Mireles James (2015)

Applications of Mathematics

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This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained...

A discrete phenomenon in propagation of $C^{\infty}$ singularities

Paul Godin (1987)

Banach Center Publications

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Projective abelian Hopf algebras over a field

Andrzej Skowroński

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CONTENTSIntroduction............................................................................................................................................51. Cohen schemes.................................................................................................................................72. Projective abelian Hopf algebras......................................................................................................113. The structure of groups $H o m_{ℋ ₁} (^{m} P,^{n} P)$ ..............................................................................174....

Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring

William W. Adams, Philippe Loustaunau, Victor P. Palamodov, Daniele C. Struppa (1997)

Annales de l'institut Fourier

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In this paper we prove that the projective dimension of $ℳ_{n} = R^{4} / ⟨ A_{n} ⟩$ is $2 n - 1$ , where $R$ is the ring of polynomials in $4 n$ variables with complex coefficients, and $⟨ A_{n} ⟩$ is the module generated by the columns of a $4 \times 4 n$ matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of $n$ quaternionic variables. As a corollary we show that the sheaf $ℛ$ of regular functions has flabby dimension $2 n - 1$ , and we prove a cohomology vanishing theorem...

$n$ -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

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Let $R$ be a graded ring and $n \geq 1$ an integer. We introduce and study $n$ -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that $n$ -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be $m$ -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever $n > m$ . Many properties of the $n$ -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized....

Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables

Janusz Gwoździewicz, Arkadiusz Płoski (2005)

Colloquium Mathematicae

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For every polynomial F in two complex variables we define the Łojasiewicz exponents $ℒ_{p, t} (F)$ measuring the growth of the gradient ∇F on the branches centered at points p at infinity such that F approaches t along γ. We calculate the exponents $ℒ_{p, t} (F)$ in terms of the local invariants of singularities of the pencil of projective curves associated with F.

On second order Thom-Boardman singularities

László M. Fehér, Balázs Kőműves (2006)

Fundamenta Mathematicae

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We derive closed formulas for the Thom polynomials of two families of second order Thom-Boardman singularities $Σ^{i, j}$ . The formulas are given as linear combinations of Schur polynomials, and all coefficients are nonnegative.

$μ$ -constant monodromy groups and marked singularities

Claus Hertling (2011)

Annales de l’institut Fourier

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$μ$ -constant families of holomorphic function germs with isolated singularities are considered from a global perspective. First, a monodromy group from all families which contain a fixed singularity is studied. It consists of automorphisms of the Milnor lattice which respect not only the intersection form, but also the Seifert form and the monodromy. We conjecture that it contains all such automorphisms, modulo $\pm id$ . Second, marked singularities are defined and global moduli...

Weighted $L^{\infty}$ -estimates for Bergman projections

José Bonet, Miroslav Engliš, Jari Taskinen (2005)

Studia Mathematica

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We consider Bergman projections and some new generalizations of them on weighted $L^{\infty} ()$ -spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.

The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity

Trond Stølen Gustavsen, Runar Ile (2011)

Banach Center Publications

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Let X be a quotient surface singularity, and define $G^{d e f} (X, r)$ as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of $G^{d e f} (X, r)$ is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove...

A boundedness theorem for morphisms between threefolds

Ekatarina Amerik, Marat Rovinsky, Antonius Van de Ven (1999)

Annales de l'institut Fourier

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The main result of this paper is as follows: let $X, Y$ be smooth projective threefolds (over a field of characteristic zero) such that $b_{2} (X) = b_{2} (Y) = 1$ . If $Y$ is not a projective space, then the degree of a morphism $f : X \to Y$ is bounded in terms of discrete invariants of $X$ and $Y$ . Moreover, suppose that $X$ and $Y$ are smooth projective $n$ -dimensional with cyclic Néron-Severi groups. If $c_{1} (Y) = 0$ , then the degree of $f$ is bounded iff $Y$ is not a flat variety. In particular, to prove our main theorem we show the non-existence of...

Existence of Gorenstein projective resolutions and Tate cohomology

Peter Jørgensen (2007)

Journal of the European Mathematical Society

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Existence of proper Gorenstein projective resolutions and Tate cohomology is proved over rings with a dualizing complex. The proofs are based on Bousfield Localization which is originally a method from algebraic topology.

Polynomial functions on the classical projective spaces

Yu. I. Lyubich, O. A. Shatalova (2005)

Studia Mathematica

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The polynomial functions on a projective space over a field = ℝ, ℂ or ℍ come from the corresponding sphere via the Hopf fibration. The main theorem states that every polynomial function ϕ(x) of degree d is a linear combination of “elementary” functions ${| ⟨ x, \cdot ⟩ |}^{d}$ .