Search results for "Lefschetz"

showing 2 items of 2 documents

Linear quotients of Artinian Weak Lefschetz algebras

2013

Abstract We study the Hilbert function and the graded Betti numbers for “generic” linear quotients of Artinian standard graded algebras, especially in the case of Weak Lefschetz algebras. Moreover, we investigate a particular property of Weak Lefschetz algebras, the Betti Weak Lefschetz Property, which makes possible to completely determine the graded Betti numbers of a generic linear quotient of such algebras.

Discrete mathematicsPure mathematicsHilbert series and Hilbert polynomialAlgebra and Number TheoryProperty (philosophy)Mathematics::Commutative AlgebraBetti numberBetti Weak Lefschetz PropertyMathematics::Rings and AlgebrasArtinian algebraLinear quotientWeak Lefschetz Propertysymbols.namesakeQuotientWeak Lefschetz; Artinian algebra; QuotientsymbolsWeak Lefschetz Property Artinian algebra Linear quotientLefschetz fixed-point theoremWeak LefschetzMathematics::Symplectic GeometryQuotientMathematics
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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.

LefschetzHistoryMathematics(all)Italian school of algebraic geometryGeneral MathematicsZariskiAlgebraic geometryCoolidgeFocus (linguistics)Algebraic geometryAlgebraDevelopment (topology)Italian school of algebraic geometryAlgebraic numberMathematicsHistoria Mathematica
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