Globally invertible differentiable or holomorphic maps
Gluing Cohen-Macaulay modules with applications to quasihomogeneous complete intersections with isolated singularities.
Gluing complex discs to Lagrangian manifolds by Gromov’s method
The paper discusses some aspects of Gromov’s theory of gluing complex discs to Lagrangian manifolds.
Gluing of differentiable spaces and applications.
Good-irreducible inner functions on a polydisc
An explicit formula is developed for Nevanlinna class functions whose behaviour at the boundary is “sufficiently rational” and is then used to deduce the uniqueness of the factorization of such inner functions. A generalization of a theorem of Frostman is given and the above results are then applied to the construction of good and/or irreducible inner functions on a polydisc.
Gradients des fonctions intérieures dans la boule unité de ...n.
Graph theoretic techniques in algebraic geometry II: construction of singular complex surfaces of the rational cohomology type of CP2.
Graphs with multiple sheeted pluripolar hulls
We study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.
Grassmann duality for -modules
Grauert's line bundle convexity, reduction and Riemann domains
We consider a convexity notion for complex spaces with respect to a holomorphic line bundle over . This definition has been introduced by Grauert and, when is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if separates each point of , then can be realized as a Riemann domain over the complex projective space...
Grauert's theorem for subanalytic open sets in real analytic manifolds
By an open neighbourhood in ℂⁿ of an open subset Ω of ℝⁿ we mean an open subset Ω' of ℂⁿ such that ℝⁿ ∩ Ω' = Ω. A well known result of H. Grauert implies that any open subset of ℝⁿ admits a fundamental system of Stein open neighbourhoods in ℂⁿ. Another way to state this property is to say that each open subset of ℝⁿ is Stein. We shall prove a similar result in the subanalytic category: every subanalytic open subset in a paracompact real analytic manifold M admits a fundamental system of subanalytic...
Green functions, Segre numbers, and King’s formula
Let be a coherent ideal sheaf on a complex manifold with zero set , and let be a plurisubharmonic function such that locally at , where is a tuple of holomorphic functions that defines . We give a meaning to the Monge-Ampère products for , and prove that the Lelong numbers of the currents at coincide with the so-called Segre numbers of at , introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, we show that satisfy a certain generalization...
Gröbner δ-bases and Gröbner bases for differential operators
This paper deals with the notion of Gröbner δ-base for some rings of linear differential operators by adapting the works of W. Trinks, A. Assi, M. Insa and F. Pauer. We compare this notion with the one of Gröbner base for such rings. As an application we give some results on finiteness and on flatness of finitely generated left modules over these rings.
Gromov–Witten invariants for mirror orbifolds of simple elliptic singularities
We consider a mirror symmetry of simple elliptic singularities. In particular, we construct isomorphisms of Frobenius manifolds among the one from the Gromov–Witten theory of a weighted projective line, the one from the theory of primitive forms for a universal unfolding of a simple elliptic singularity and the one from the invariant theory for an elliptic Weyl group. As a consequence, we give a geometric interpretation of the Fourier coefficients of an eta product considered by K. Saito.
Group actions and envelopes of holomorphy.
Groupe de monodromie géométrique des singularités simples.
Groupes de cohomologie d'un fibré holomorphe à base et à fibre de Stein.
Groupes triangulaires lagrangiens en géométrie hyperbolique complexe
Nous présentons quelques résultats au sujet des groupes engendrés par trois involutions antiholomorphes dans le cadre du plan hyperbolique complexe .
Groups of transformations of a G-structure whic H leave invariant a substructure.
Growth at infinity of a polynomial with a compact zero set