Let \( k \) be a field and \( A \) a (standard) graded Artinian \( k \)-algebra. \( A \) is said to have the Weak Lefschetz Property (WLP) if multiplication by a general linear form \( \times l \colon A_i \rightarrow A_{i+1} \) is full rank for all \( i \geq 0 \). We also say \( A \) has the Strong Lefschetz Property (SLP) if multiplication by powers of a general linear form \( \times l^d \colon A_i \rightarrow A_{i+d} \) is full rank for all \( i \geq 0 \) and for all \( d \geq 0\). Note that if \( A \) has the SLP, then \( A \) also has the WLP.

While this page is under construction, please see Betti tables forcing failure of the Weak Lefschetz Property for some results.

Joint work with Hal Schenck.