Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/113296
 Title: Lefschetz properties in algebra and geometry Author: Salat Moltó, Martí Director: Miró-Roig, Rosa M. (Rosa Maria) Keywords: Àlgebra commutativaTreballs de fi de grauGeometria algebraicaSingularitats (Matemàtica)Anells artiniansCommutative algebraBachelor's thesisAlgebraic geometrySingularities (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 URI: http://hdl.handle.net/2445/113296 Appears in Collections: Treballs Finals de Grau (TFG) - Matemàtiques

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