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memoria.pdf (364.96 KB)

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Bachelor thesis

Publication date

2017-01-16

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cc-by-nc-nd (c) Martí Salat Moltó, 2017
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/113296

Lefschetz properties in algebra and geometry

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Rosa Maria Miró-Roig

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Àlgebra commutativa, Treballs de fi de grau, Geometria algebraica, Singularitats (Matemàtica), Anells artinians

Subject (English)

Commutative algebra, Bachelor's theses, Algebraic geometry, Singularities (Mathematics), Artin rings

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

SALAT MOLTÓ, Martí. Lefschetz properties in algebra and geometry. [consulted: 14 of August of 2026]. Available at: https://hdl.handle.net/2445/113296

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