Laura Casabella

Goethe-Universität Frankfurt

The variety of orthogonal frames

The variety of orthogonal frames $V(d,n)$ parameterizes $n$-tuples of pairwise orthogonal vectors in a $d$-dimensional quadratic vector space. We study the variety $V(d,n)$ and its irreducibility, reducedness, normality, factoriality, and being a complete intersection in terms of $d$ and $n$. Our results give applications to Lovasz-Saks-Schrijver ideals of graphs, and improve bounds of Conca-Welker (2019) and Tolosa Villarreal (2025). Joint work with Alessio Sammartano.