Hypergraph LSS-ideals and coordinate sections of symmetric tensors

Abstract

Let be a field, and be a hypergraph. For an integer the Lovász-Saks-Schrijver ideal (LSS-ideal) is the ideal generated by the polynomials for edges e of H. In this paper for an algebraically closed field and a k-uniform hypergraph we employ a connection between LSS-ideals and coordinate sections of the closure of the set of homogeneous degree k symmetric tensors in n variables of to derive results on the irreducibility of its coordinate sections. To this end we provide results on primality and the complete intersection property of . We then use the combinatorial concept of positive matching decomposition of a hypergraph H to provide bounds on when turns prime to provide results on the irreducibility of coordinate sections of .