#### 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.

Done