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http://hdl.handle.net/2445/113296
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 theses 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 |
URI: | http://hdl.handle.net/2445/113296 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 364.96 kB | Adobe PDF | View/Open |
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