Sourjya Banerjee

Institute of Mathematical Sciences, Chennai

Unimodular rows over real algebraic varieties

In a commutative ring $R$, a unimodular row of length $n$ is an $n$-tuple whose entries generate the whole ring $R$. The group of all $n \times n$ invertible matrices over $R$ acts naturally on the set of all unimodular rows of length $n$. In certain favourable situations, the corresponding orbit space admits the structure of an abelian group. In this talk, we discuss this orbit space in the case where the ring arises as the coordinate ring of a real algebraic variety.