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A bound for the Milnor number of plane curve singularities

Arkadiusz Płoski (2014)

Open Mathematics

Let f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize the curves f = 0 for which μ0(f) = (d−1)2 − [d/2].

A characterization of quasi-homogeneous Gorenstein surface singularities

Jonathan M. Wahl (1985)

Compositio Mathematica

A class of non-rational surface singularities with bijective Nash map

Camille Plénat, Patrick Popescu-Pampu (2006)

Bulletin de la Société Mathématique de France

Let $(𝒮, 0)$ be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor $E$ and its irreducible components $E_{i}$ , $i \in I$ . The Nash map associates to each irreducible component $C_{k}$ of the space of arcs through $0$ on $𝒮$ the unique component of $E$ cut by the strict transform of the generic arc in $C_{k}$ . Nash proved its injectivity and asked if it was bijective. As a particular case of our main theorem, we prove that this is the case if $E \cdot E_{i} < 0$ for any $i \in I$ .

A contribution to the theory of tacnodal quartics

Dalibor Klucký, Libuše Marková (1985)

Časopis pro pěstování matematiky

A note on Bézout's theorem

Sławomir Rams, Piotr Tworzewski, Tadeusz Winiarski (2005)

Annales Polonici Mathematici

We present a version of Bézout's theorem basing on the intersection theory in complex analytic geometry. Some applications for products of surfaces and curves are also given.

A numerical criterion for the permissibility of a blowing-up

Balwant Singh (1976)

Compositio Mathematica

A period mapping for certain semi-universal deformations

Eduard Looijenga (1975)

Compositio Mathematica

A propos du problème des arcs de Nash

Camille Plénat (2005)

Annales de l’institut Fourier

Soit $ℋ = ⋃ N_{i}$ la décomposition canonique de l’espace des arcs $ℋ$ passant par une singularité normale de surface. Dans cet article, on propose deux nouvelles conditions qui si elles sont vérifiées permettent de montrer que $N_{i}$ n’est pas inclus dans $N_{j}$ . On applique ces conditions pour donner deux nouvelles preuves du problème de Nash pour les singularités sandwich minimales.

A regulator map for singular varieties.

Hélène Esnault (1990)

Mathematische Annalen

A result on the comparison principle for the log canonical threshold of plurisubharmonic functions

Hai Mau Le, Hong Xuan Nguyen, Hung Viet Vu (2014)

Annales Polonici Mathematici

We prove a comparison principle for the log canonical threshold of plurisubharmonic functions under an assumption on complex Monge-Ampère measures.

A singular Riemann-Roch for Hirzebruch characteristics

Shoji Yokura (1998)

Banach Center Publications

Abelian group actions on algebraic varieties with one fixed point.

F. Knop, Amir H. Assadi, R. Barlow (1992)

Mathematische Zeitschrift

Altérations de variétés algébriques

Pierre Berthelot (1995/1996)

Séminaire Bourbaki

Ambient Deformations for Exceptional Sets in Two-Manifolds.

Henry B. Laufer (1979)

Inventiones mathematicae

Ample vector bundles on singular varieties.

Qi Zhang (1995)

Mathematische Zeitschrift

An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

H.-Ch. Graf von Bothmer, Wolfgang Ebeling, Xavier Gómez-Mont (2008)

Annales de l’institut Fourier

Let $(V, 0)$ be a germ of a complete intersection variety in $ℂ^{n + k}$ , $n > 0$ , having an isolated singularity at $0$ and $X$ be the germ of a holomorphic vector field having an isolated zero at $0$ and tangent to $V$ . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of $X$ is also isolated in the ambient space $ℂ^{n + k}$ we give a formula for the homological index in terms of local linear algebra.

Currently displaying 1 – 20 of 31

Page 1 Next

Displaying 1 – 20 of 31

A bound for the Milnor number of plane curve singularities

A characterization of quasi-homogeneous Gorenstein surface singularities

A class of non-rational surface singularities with bijective Nash map

A contribution to the theory of tacnodal quartics

A note on Bézout's theorem

A numerical criterion for the permissibility of a blowing-up

A period mapping for certain semi-universal deformations

A propos du problème des arcs de Nash

A regulator map for singular varieties.

A result on the comparison principle for the log canonical threshold of plurisubharmonic functions

A singular Riemann-Roch for Hirzebruch characteristics

Abelian group actions on algebraic varieties with one fixed point.

Altérations de variétés algébriques

Ambient Deformations for Exceptional Sets in Two-Manifolds.

Ample vector bundles on singular varieties.

An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

An arithmetic characterisation of the symmetric monodromy groups of singularities.

An example concerning a question of Zariski

An extension to fields of positive characteristic of Mather's construction of the Thom-Boardman sequence

An Integral Criterion for the Equivalence of Plane Curves.

Currently displaying 1 – 20 of 31