Nakamaye’s theorem on log canonical pairs

Salvatore Cacciola; Angelo Felice Lopez

Displaying similar documents to “Nakamaye’s theorem on log canonical pairs”

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

Paul Godin (1987)

Banach Center Publications

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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...

Plurisubharmonic functions with logarithmic singularities

E. Bedford, B. A. Taylor (1988)

Annales de l'institut Fourier

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To a plurisubharmonic function $u$ on $C^{n}$ with logarithmic growth at infinity, we may associate the Robin function $ρ_{u} (z) = \underset{λ \to \infty}{lim sup} u (λ z) - log (λ z)$ defined on $P^{n - 1}$ , the hyperplane at infinity. We study the classes $L_{+}$ , and (respectively) $L_{p}$ of plurisubharmonic functions which have the form $u = log (1 + | z |) + O (1)$ and (respectively) for which the function $ρ_{u}$ is not identically $- \infty$ . We obtain an integral formula which connects the Monge-Ampère measure on the space $C^{n}$ with the Robin function on $P^{n - 1}$ . As an application we obtain a criterion...

$μ$ -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...

Jacobian discrepancies and rational singularities

Tommaso de Fernex, Roi Docampo (2014)

Journal of the European Mathematical Society

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Inspired by several works on jet schemes and motivic integration, we consider an extension to singular varieties of the classical definition of discrepancy for morphisms of smooth varieties. The resulting invariant, which we call $𝐽𝑎𝑐𝑜𝑏𝑖𝑎𝑛𝑑𝑖𝑠𝑐𝑟𝑒𝑝𝑎𝑛𝑐𝑦$ , is closely related to the jet schemes and the Nash blow-up of the variety. This notion leads to a framework in which adjunction and inversion of adjunction hold in full generality, and several consequences are drawn from these properties. The main result...

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.

Covers in $p$ -adic analytic geometry and log covers I: Cospecialization of the $(p^{'})$ -tempered fundamental group for a family of curves

Emmanuel Lepage (2013)

Annales de l’institut Fourier

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The tempered fundamental group of a $p$ -adic analytic space classifies covers that are dominated by a topological cover (for the Berkovich topology) of a finite étale cover of the space. Here we construct cospecialization homomorphisms between $(p^{'})$ versions of the tempered fundamental groups of the fibers of a smooth family of curves with semistable reduction. To do so, we will translate our problem in terms of cospecialization morphisms of fundamental groups of the log fibers of the log...

Note on special arithmetic and geometric means

Horst Alzer (1994)

Commentationes Mathematicae Universitatis Carolinae

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We prove: If $A (n)$ and $G (n)$ denote the arithmetic and geometric means of the first $n$ positive integers, then the sequence $n \mapsto n A (n) / G (n) - (n - 1) A (n - 1) / G (n - 1)$ $(n \geq 2)$ is strictly increasing and converges to $e / 2$ , as $n$ tends to $\infty$ .

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...

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.

Inequalities for Taylor series involving the divisor function

Horst Alzer, Man Kam Kwong (2022)

Czechoslovak Mathematical Journal

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Let $T (q) = \sum_{k = 1}^{\infty} d (k) q^{k}, | q | < 1,$ where $d (k)$ denotes the number of positive divisors of the natural number $k$ . We present monotonicity properties of functions defined in terms of $T$ . More specifically, we prove that $H (q) = T (q) - \frac{log (1 - q)}{log (q)}$ is strictly increasing on $(0, 1)$ , while $F (q) = \frac{1 - q}{q} H (q)$ is strictly decreasing on $(0, 1)$ . These results are then applied to obtain various inequalities, one of which states that the double inequality $α \frac{q}{1 - q} + \frac{log (1 - q)}{log (q)} < T (q) < β \frac{q}{1 - q} + \frac{log (1 - q)}{log (q)}, 0 < q < 1,$ holds with the best possible constant factors $α = γ$ and $β = 1$ . Here, $γ$ denotes Euler’s constant. This refines a result of Salem, who...

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.