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Title: Lefschetz properties in algebra and geometry
Author: Salat Moltó, Martí
Director/Tutor: Miró-Roig, Rosa M. (Rosa Maria)
Keywords: Àlgebra commutativa
Treballs de fi de grau
Geometria algebraica
Singularitats (Matemàtica)
Anells artinians
Commutative algebra
Bachelor's thesis
Algebraic geometry
Singularities (Mathematics)
Artin rings
Issue Date: 16-Jan-2017
Abstract: The weak and strong Lefschetz properties on graded artinian algebras have been an object of study along the last few decades. Precisely, let be $A$ a graded artinian algebra. We say that $A$ has the Strong Lefschetz property (SLP) if the multiplication by a $d$th power of a general linear form have maximal rank (i.e. $\times L^{d} : A_{i} \rightarrow A_{i+d}$ is injective or surjective for every $i$). We say that $A$ has the Weak Lefschetz property (WLP) if occurs the same with $d = 1$. These properties have connections among different areas such as algebraic geometry, commutative algebra and combinatorics. Sometimes quite surprising, these connections give new approaches and relate problems, a priori, very distant.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Rosa Maria Miró-Roig
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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