Endliche Automorphismengruppen analytischer ℂ-Algebren und ihre invarianten

1982

Resolution of Weighted Homogeneous Surface Singularities

2000

The purpose of this article is to review the method of Orlik and Wagreich to resolve normal singularities on weighted homogeneous surfaces X. Moreover, we explain the description of such surfaces by automorphy factors due to Dolgachev and Pinkham.

Remarks on iteration of formal automorphisms

1988

Etude de l'iteration des automorphismes formels. Generalisation et interpretation d'un critere de Reich-Schwaiger

Dependence on nuclear factor of activated T-cells (NFAT) levels discriminates conventional T cells from Foxp3 + regulatory T cells

2012

Several lines of evidence suggest nuclear factor of activated T-cells (NFAT) to control regulatory T cells: thymus-derived naturally occurring regulatory T cells (nTreg) depend on calcium signals, the Foxp3 gene harbors several NFAT binding sites, and the Foxp3 (Fork head box P3) protein interacts with NFAT. Therefore, we investigated the impact of NFAT on Foxp3 expression. Indeed, the generation of peripherally induced Treg (iTreg) by TGF-β was highly dependent on NFAT expression because the ability of CD4 + T cells to differentiate into iTreg diminished markedly with the number of NFAT family members missing. It can be concluded that the expression of Foxp3 in TGF-β–induced iTreg depends…

A rank theorem for analytic maps between power series spaces

1994

The cancellation property for direct products of analytic space germs

1990

Affine varieties and lie algebras of vector fields

1993

In this article, we associate to affine algebraic or local analytic varieties their tangent algebra. This is the Lie algebra of all vector fields on the ambient space which are tangent to the variety. Properties of the relation between varieties and tangent algebras are studied. Being the tangent algebra of some variety is shown to be equivalent to a purely Lie algebra theoretic property of subalgebras of the Lie algebra of all vector fields on the ambient space. This allows to prove that the isomorphism type of the variety is determinde by its tangent algebra.

Endliche Automorphismengruppen von direkten Produkten komplexer Raumkeime

1985

Actions of complex Lie groups on analytic ?-algebras

1987

On a reduced analytic .ℂ-algebraR there are faithful analytic actions of complex Lie groups of arbitrarily high dimension if and only ifR has Krull dimension ≥2.

Semi-Universal unfoldings and orbits of the contact group

1996

The Lie algebra of polynomial vector fields and the Jacobian conjecture

1998

The Jacobian conjecture for polynomial maps ϕ:Kn→Kn is shown to be equivalent to a certain Lie algebra theoretic property of the Lie algebra\(\mathbb{D}\) of formal vector fields inn variables. To be precise, let\(\mathbb{D}_0 \) be the unique subalgebra of codimensionn (consisting of the singular vector fields),H a Cartan subalgebra of\(\mathbb{D}_0 \),Hλ the root spaces corresponding to linear forms λ onH and\(A = \oplus _{\lambda \in {\rm H}^ * } H_\lambda \). Then every polynomial map ϕ:Kn→Kn with invertible Jacobian matrix is an automorphism if and only if every automorphism Φ of\(\mathbb{D}\) with Φ(A)\( \subseteq A\) satisfies Φ(A)=A.

The Herzog-Vasconcelos conjecture for affine semigroup rings

1999

Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.

Automorphisms of direct products of algebroid spaces

1991

Algebraic singularities have maximal reductive automorphism groups

1989

LetX = On/ibe an analytic singularity where ṫ is an ideal of theC-algebraOnof germs of analytic functions on (Cn, 0). Letdenote the maximal ideal ofXandA= AutXits group of automorphisms. An abstract subgroupequipped with the structure of an algebraic group is calledalgebraic subgroupofAif the natural representations ofGon all “higher cotangent spaces”are rational. Letπbe the representation ofAon the first cotangent spaceandA1=π(A).

Analytic curves in power series rings

1990

Automorphisms of simplicial complexes and their Stanley-Reisner rings

1997