$F$-pure threshold for the symmetric determinantal ring

Abstract

We give a value for the $F$-pure threshold at the maximal homogeneous ideal $\mathfrak{m}$ of the symmetric determinantal ring over a field of prime characteristic. The answer is characteristic independent, so we immediately get the log canonical threshold in characteristic zero as well.

Final version. Contents of section 2.1 of pervious version has been moved to the introduction. Accepted for publication in Communications in Algebra