# name
Lefschetz properties in algebra and geometry

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Rosa Maria Miró-Roig

# metadata.dc.description.abstract[].value
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.

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Lefschetz properties in algebra and geometry