The Euler number of the normalization of an algebraic threefold with ordinary singularities

Shoji Tsuboi

Displaying similar documents to “The Euler number of the normalization of an algebraic threefold with ordinary singularities”

Smooth double subvarieties on singular varieties, III

M. R. Gonzalez-Dorrego (2016)

Banach Center Publications

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Let k be an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, r ∈ ℕ, where S and F are two surfaces and all the singularities of F are of the form $z ³ = x^{3 s} - y^{3 s}$ , s ∈ ℕ. We prove that C can never pass through such kind of singularities of a surface, unless r = 3a, a ∈ ℕ. We study multiplicity-r structures on varieties r ∈ ℕ. Let Z be a reduced irreducible nonsingular (n-1)-dimensional variety such that rZ = X ∩ F, where X is a normal n-fold, F...

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

Paul Godin (1987)

Banach Center Publications

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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...

Singularities of Maxwell’s system in non-hilbertian Sobolev spaces

Wided Chikouche, Serge Nicaise (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in $L^{p} {(Ω)}^{2}$ . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space $W^{2, p} {(Ω)}^{2}$ and an explicit singular one.

The end curve theorem for normal complex surface singularities

Walter D. Neumann, Jonathan Wahl (2010)

Journal of the European Mathematical Society

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We prove the “End Curve Theorem,” which states that a normal surface singularity $(X, o)$ with rational homology sphere link $Σ$ is a splice quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end curve function” is an analytic function $(X, o) \to (ℂ, 0)$ whose zero set intersects $Σ$ in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf. A “splice quotient singularity” $(X, o)$ is described by giving an explicit set of...

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.

Cobordisms of fold maps of 2k+2-manifolds into $ℝ^{3 k + 2}$

Tamás Terpai (2008)

Banach Center Publications

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We calculate the group of cobordisms of k-codimensional maps into Euclidean space with no singularities more complicated than fold for a 2k+2-dimensional source manifold in both oriented and unoriented cases.

Singularities of k-tuples of vector fields

Bronisław Jakubczyk, Feliks Przytycki

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CONTENTSIntroduction............................................................................51. The main ideas and results................................................62. $H^{n, k}$ -invariant subsets of $ℋ^{n, k}$ .........................223. Reduction to germs of differential 1-forms........................354. The case k ≥ 2n-3. Proof of Theorem A...........................445. The case n = 3, k = 2.......................................................46Appendix. Connections with control theory...........................59List...

Thom polynomials and Schur functions: the singularities $I I I_{2, 3} (-)$

Özer Öztürk (2010)

Annales Polonici Mathematici

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We give a closed formula for the Thom polynomials of the singularities $I I I_{2, 3} (-)$ in terms of Schur functions. Our computations combine the characterization of the Thom polynomials via the “method of restriction equations” of Rimányi et al. with the techniques of Schur functions.

On the classification of real mono-germs of corank one and codimension one

Kevin Houston (2004)

Banach Center Publications

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Corank one mono-germs $f : (ℝ ⁿ, 0) \to (ℝ^{p}, 0)$ , n < p, of $_{e}$ -codimension one are classified by giving an explicit normal form.

Singular nonlinear problem for ordinary differential equation of the second order

Irena Rachůnková, Jan Tomeček (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The paper deals with the singular nonlinear problem $u^{''} (t) + f (t, u (t), u^{'} (t)) = 0, u (0) = 0, u^{'} (T) = ψ (u (T)),$ where $f \in 𝐶𝑎𝑟 ((0, T) \times D)$ , $D = (0, \infty) \times$ . We prove the existence of a solution to this problem which is positive on $(0, T]$ under the assumption that the function $f (t, x, y)$ is nonnegative and can have time singularities at $t = 0$ , $t = T$ and space singularity at $x = 0$ . The proof is based on the Schauder fixed point theorem and on the method of a priori estimates.

Singular $φ$ -Laplacian third-order BVPs with derivative dependance

Smaïl Djebali, Ouiza Saifi (2016)

Archivum Mathematicum

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This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a $φ$ -Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotonic with respect to its arguments and may have a space singularity; however no Nagumo type condition...

Instanton Singularities in Euclidean $Φ^{4}$ Quantum Field Theories

J. Feldman (1986)

Recherche Coopérative sur Programme n°25

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Springer fiber components in the two columns case for types $A$ and $D$ are normal

Nicolas Perrin, Evgeny Smirnov (2012)

Bulletin de la Société Mathématique de France

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We study the singularities of the irreducible components of the Springer fiber over a nilpotent element $N$ with $N^{2} = 0$ in a Lie algebra of type $A$ or $D$ (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen–Macaulay, and have rational singularities.

Nakamaye’s theorem on log canonical pairs

Salvatore Cacciola, Angelo Felice Lopez (2014)

Annales de l’institut Fourier

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We generalize Nakamaye’s description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension $\leq 1$ . We also generalize Ein-Lazarsfeld-Mustaţă-Nakamaye-Popa’s description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.

Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs

Victor V. Batyrev (1999)

Journal of the European Mathematical Society

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Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata log-terminal pair corresponding to an algebraic variety $V$ having a regular action of a finite group $G$ . In this situation we show that the stringy Euler number of this pair coincides with the physicists’ orbifold Euler number defined by the Dixon-Harvey-Vafa-Witten formula. As an application, we...

On the principle of real moduli flexibility: perfect parametrizations

Edoardo Ballico, Riccardo Ghiloni (2014)

Annales Polonici Mathematici

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Let V be a real algebraic manifold of positive dimension. The aim of this paper is to show that, for every integer b (arbitrarily large), there exists a trivial Nash family $= {V_{y}}_{y \in R^{b}}$ of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over $y \in R^{b} ∖ 0$ (possibly singular over y = 0) and is perfectly parametrized by $R^{b}$ in the sense that $V_{y}$ is birationally nonisomorphic to $V_{z}$ for every $y, z \in R^{b}$ with y ≠ z. A similar result continues to hold if V is a singular real algebraic...

Cycles on algebraic models of smooth manifolds

Wojciech Kucharz (2009)

Journal of the European Mathematical Society

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Every compact smooth manifold $M$ is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of $M$ . We study modulo 2 homology classes represented by algebraic subsets of $X$ , as $X$ runs through the class of all algebraic models of $M$ . Our main result concerns the case where $M$ is a spin manifold.

Interpolation of $κ$ -compactness and PCF

István Juhász, Zoltán Szentmiklóssy (2009)

Commentationes Mathematicae Universitatis Carolinae

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We call a topological space $κ$ -compact if every subset of size $κ$ has a complete accumulation point in it. Let $Φ (μ, κ, λ)$ denote the following statement: $μ < κ < λ = cf (λ)$ and there is ${S_{ξ} : ξ < λ} \subset {[κ]}^{μ}$ such that $| {ξ : | S_{ξ} \cap A | = μ} | < λ$ whenever $A \in {[κ]}^{< κ}$ . We show that if $Φ (μ, κ, λ)$ holds and the space $X$ is both $μ$ -compact and $λ$ -compact then $X$ is $κ$ -compact as well. Moreover, from PCF theory we deduce $Φ (cf (κ), κ, κ^{+})$ for every singular cardinal $κ$ . As a corollary we get that a linearly Lindelöf and $ℵ_{ω}$ -compact space is uncountably compact, that is $κ$ -compact for all uncountable cardinals...