arXiv subjects

Amith Shastri K

Publications and source records attributed to Amith Shastri K.

2 recordsLinked to original sources

arXiv2022

Jacobians, Anti-affine groups and torsion points

We give criteria for the Jacobian of a singular curve $X$ with at most ordinary $n$-point singularities to be anti-affine. In particular, for the case of curves with single ordinary double point we exhibit a relation with torsion divisors. If the geometric genus of the singular curve is atleast 3 and the normalization is non-hyperelliptic and non-bielliptic, then except for finitely many cases the Jacobian of $X$ is anti-affine. Furthermore, if the normalization is a general curve of genus atleast 3 then the Jacobian of $X$ is always anti-affine.

math.AG↗

arXiv2018

Character on a homogeneous space

In this paper we look at the notion of cohomological triviality of fibrations of homogeneous spaces of affine algebraic groups defined over $\mathbb{C}$ and use topological methods, primarily the theory of covering spaces. This is made possible because of the structure theory of affine algebraic groups. Further, we generalize our results for arbitrary connected algebraic groups and their homogeneous spaces. As an application of our methods, we give a structure result for quasi-reductive algebraic groups(i.e groups whose unipotent radical is trivial), upto isogeny.

math.AG↗