Abstract: In 1978, Stanley constructs an example of an Artinian Gorenstein (AG) ring A with non-unimodal H-vector (1, 13, 12, 13, 1). Migliore-Zanello showed that for regularity r = 4, Stanley’s example has the smallest possible codimension c for an AG ring with non-unimodal H-vector. The weak Lefschetz property (WLP) has been much studied for AG rings; it is easy to show that an AG ring with non-unimodal H-vector fails to have WLP. In codimension c = 3 it is conjectured that all AG rings have WLP. For c = 4, Gondim showed that WLP always holds for r ≤ 4 and gives a family where WLP fails for any r ≥ 7, building on an earlier example of Ikeda of failure for r = 5. In this note we study the minimal free resolution of A and relation to Lefschetz properties (both weak and strong) and Jordan type for c = 4 and r ≤ 6.

12:15pm, 511 Lake Hall, Nancy Abdallah (University of Borås)