Alladi Ramakrishnan Hall

Properness of degenerate quadratic bundles

Yeshonidhi Pandey

IISER, Mohali

Let $q: Sym^2 V -> \mathcal{O}_X $ be a vector bundle equipped
with a quadratic form on a smooth projective curve $X$. We assume that $q$
is only generically non-degenerate. This is the most relevant case when
$deg(V)<0$. When one tries to make a GIT construction of the moduli of
such pairs, then there are technical difficulties in the Hilbert-Mumford
criterion. This motivates our alternative method of directly showing
that a certain functor is proper. In the `limit at infinity' we find
everywhere degenerate quadratic forms.