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Mather discrepancy and the arc spaces

Shihoko Ishii (2013)

Annales de l’institut Fourier

A goal of this paper is a characterization of singularities according to a new invariant, Mather discrepancy. We also show some evidences convincing us that Mather discrepancy is a reasonable invariant in a view point of birational geometry.

Matrice magique associée à un germe de courbe plane et division par l’idéal jacobien

Joël Briançon, Philippe Maisonobe, Tristan Torrelli (2007)

Annales de l’institut Fourier

Nous nous donnons, dans l’anneau des germes de fonctions holomorphes à l’origine de ℂ 2 , une fonction f définissant une singularité isolée et nous nous intéressons à l’équation u f x ′ + v f y ′ = w f , lorsque la fonction w est donnée. Nous introduisons les multiplicités d’intersection relatives de w et f y ′ le long des branches de f et nous étudions les solutions à l’aide de ces valuations. Grâce aux résultats ainsi démontrés, nous construisons explicitement une équation fonctionnelle vérifiée par f .

Modular deformations and space curve singularities.

Bernd Martin (2003)

Revista Matemática Iberoamericana

We investigate different concepts of modular deformations of germs of isolated singularities (infinitesimal, Artinian, formal). An obstruction calculus based on the graded Lie algebra structure of the tangent cohomology for modular dcformations is introduced. As the main result the characterisation of the maximal infinitesimally modular subgerm of the miniversal family as flattening stratum of the relative Tjurina module is extended from ICIS to space curve singularities.

Modules and quiver representations whose orbit closures are hypersurfaces

Nguyen Quang Loc, Grzegorz Zwara (2014)

Colloquium Mathematicae

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite-dimensional A-modules whose orbit closures are local hypersurfaces. The result is reduced to an analogous characterization for orbit closures of quiver representations obtained in Section 3.

Moduli of Germs of Legendrian Curves

António Araújo, Orlando Neto (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We construct the generic component of the moduli space of the germs of Legendrian curves with generic plane projection topologically equivalent to a curve y n = x m .

Monodromy of a family of hypersurfaces

Vincenzo Di Gennaro, Davide Franco (2009)

Annales scientifiques de l'École Normale Supérieure

Let Y be an ( m + 1 ) -dimensional irreducible smooth complex projective variety embedded in a projective space. Let Z be a closed subscheme of Y , and δ be a positive integer such that ℐ Z , Y ( δ ) is generated by global sections. Fix an integer d ≥ δ + 1 , and assume the general divisor X ∈ | H 0 ( Y , ℐ Z , Y ( d ) ) | is smooth. Denote by H m ( X ; ℚ ) ⊥ Z van the quotient of H m ( X ; ℚ ) by the cohomology of Y and also by the cycle classes of the irreducible components of dimension m of Z . In the present paper we prove that the monodromy representation on H m ( X ; ℚ ) ⊥ Z van for the family of smooth...

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