# Junzo Watanabe: The resultants of quadratic complete intersections and the higher Hessians of n-ary n-ic

**Time: **
Mon 2021-11-22 13.00 - 14.00

**Location: **
Zoom, meeting ID: 630 9876 5984

**Participating: **
Junzo Watanabe (Tokai University)

### Abstract

If *n* linearly independent homogenous forms are given in the polynomial ring in *n* variables, we know that it is a complete intersection by the non-vanishing of the resultant of these forms. The SLP of an Artinian Gorenstein algebra *A* can be determined by the non-vanishing of the Higher Hessians of the Macaulay dual generator *F* of *A*. If *A* is a quadratic complete intersection, *F* is a polynomial in *n* variables of degree *n*. On the other hand if *F* is a homogeneous form of degree *n* in *n* variables, the annihilator of *F* contains *n* quadratic forms. This gives us a criterion for the Ann(*F*) to be a complete intersection. Keeping these criteria in mind, I will make an attempt to construct a counter example to the long standing conjecture “If *A* is a ci, then *A* should have the SLP”.