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
.
Acknowledgments
The authors are grateful to Rashid Zaare-Nahandi for numerous suggestions and discussions.