Search results for "Zariski"
showing 4 items of 4 documents
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.
Remarks on the relations between the Italian and American schools of algebraic geometry in the first decades of the 20th century
2004
Abstract In this paper we give an overview of the interactions between Italian and American algebraic geometers during the first decades of the 20th century. We focus on three mathematicians—Julian L. Coolidge, Solomon Lefschetz, and Oscar Zariski—whose relations with the Italian school were quite intense. More generally, we discuss the importance of this influence in the development of algebraic geometry in the first half of the 20th century.
Affine Algebraic Varieties
2000
Algebraic geometers study zero loci of polynomials. More accurately, they study geometric objects, called algebraic varieties, that can be described locally as zero loci of polynomials. For example, every high school mathematics student has studied a bit of algebraic geometry, in learning the basic properties of conic sections such as parabolas and hyperbolas.
A criterion for extending morphisms from open subsets of smooth fibrations of algebraic varieties
2021
Abstract Given a smooth morphism Y → S and a proper morphism P → S of algebraic varieties we give a sufficient condition for extending an S-morphism U → P , where U is an open subset of Y, to an S-morphism Y → P , analogous to Zariski's main theorem.