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La condition “ $μ (*)$ constant” est une condition numérique d’équisingularité introduite par B. Teissier. Celui-ci a démontré dans (Astérisque, 7 & 8 (1973) II. Théorème 3.9) que cette condition implique les conditions de Whitney, nous montrons ici la réciproque.

Les singularités simples elliptiques, leurs déformations, les surfaces de del Pezzo et les transformations quadratiques

J.-Y. Mérindol (1982)

Annales scientifiques de l'École Normale Supérieure

Letter to the Editors.

B. Malgrange (1973)

Inventiones mathematicae

Lifting $D$ -modules from positive to zero characteristic

João Pedro P. dos Santos (2011)

Bulletin de la Société Mathématique de France

We study liftings or deformations of $D$ -modules ( $D$ is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic $D$ -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given $D$ -module in positive characteristic. At the end we compare the problems...

Limits of log canonical thresholds

Tommaso de Fernex, Mircea Mustață (2009)

Annales scientifiques de l'École Normale Supérieure

Let $𝒯_{n}$ denote the set of log canonical thresholds of pairs $(X, Y)$ , with $X$ a nonsingular variety of dimension $n$ , and $Y$ a nonempty closed subscheme of $X$ . Using non-standard methods, we show that every limit of a decreasing sequence in $𝒯_{n}$ lies in $𝒯_{n - 1}$ , proving in this setting a conjecture of Kollár. We also show that $𝒯_{n}$ is closed in $𝐑$ ; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in order to check...

Linear Complementary Inequalities for Orders of Germs of Analytic Functions.

Shuzo Izumi (1981/1982)

Inventiones mathematicae

Local characterization of algebraic manifolds and characterization of components of the set $S_{f}$

Zbigniew Jelonek (2000)

Annales Polonici Mathematici

We show that every n-dimensional smooth algebraic variety X can be covered by Zariski open subsets $U_{i}$ which are isomorphic to closed smooth hypersurfaces in $ℂ^{n + 1}$ . As an application we show that forevery (pure) n-1-dimensional ℂ-uniruled variety $X \subset ℂ^{m}$ there is a generically-finite (even quasi-finite) polynomial mapping $f : ℂ^{n} \to ℂ^{m}$ such that $X \subset S_{f}$ . This gives (together with [3]) a full characterization of irreducible components of the set $S_{f}$ for generically-finite polynomial mappings $f : ℂ^{n} \to ℂ^{m}$ .

Local Cohomolgy Along Exceptional Sets.

Ulrich Karras (1986)

Mathematische Annalen

Local cohomology and support for triangulated categories

Dave Benson, Srikanth B. Iyengar, Henning Krause (2008)

Annales scientifiques de l'École Normale Supérieure

We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Special cases are, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of...

Local cohomology and the connectedness dimension in algebraic varieties.

Markus Brodmann, Josef Rung (1986)

Commentarii mathematici Helvetici

Local Cohomology and the Cousin Complex for a Commutative Noetherian Ring.

Rodney Y. Sharp (1977)

Mathematische Zeitschrift

Local cohomology, cofiniteness and homological functors of modules

Kamal Bahmanpour (2022)

Czechoslovak Mathematical Journal

Let $I$ be an ideal of a commutative Noetherian ring $R$ . It is shown that the $R$ -modules $H_{I}^{j} (M)$ are $I$ -cofinite for all finitely generated $R$ -modules $M$ and all $j \in ℕ_{0}$ if and only if the $R$ -modules ${Ext}_{R}^{i} (N, H_{I}^{j} (M))$ and ${Tor}_{i}^{R} (N, H_{I}^{j} (M))$ are $I$ -cofinite for all finitely generated $R$ -modules $M$ , $N$ and all integers $i, j \in ℕ_{0}$ .

Local cohomology multiplicities in terms of étale cohomology

Manuel Blickle, Raphaël Bondu (2005)

Annales de l'institut Fourier

Using a recently introduced correspondence of Emerton-Kisin we give a description of Lyubeznik’s local cohomology invariants in terms of local étale cohomology with $𝐙 / p 𝐙$ coefficients.

Local constribution to the Lefschetz fixes point formula.

Robert MacPherson, Mark Goresky (1993)

Inventiones mathematicae

Local fundamental groups of surface singularities in characteristic p.

S.D. Cutkosky, Hema Srinivasan (1993)

Commentarii mathematici Helvetici

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