arXiv subjects

V. Balaji

Publications and source records attributed to V. Balaji.

21 records · Page 2Linked to original sources

arXiv2002

Semistable Principal Bundles-II (in positive characteristics)

Let H be a semisimple algebaric group and let X be a smooth projective curve defined over an algebraically closed field k. In the first part of this paper we show that the moduli of semistable principal H-bundles exists once given a "low-height" representation of H. We also show the projectivity of the moduli space if p > ψ, where ψis a representation theoritic index. The projectivity is a consequence of a semistable reduction theorem. The irreducibility of the moduli space of semistable H-bundles for simple and simply connected group is obtained as a consequence.

math.AG↗

arXiv1995

Stability of the Poincaré bundle

Let $C$ be a nonsingular projective curve of genus $g\ge2$ defined over the complex numbers, and let $M_ξ$ denote the moduli space of stable bundles of rank $n$ and determinant $ξ$ on $C$, where $ξ$ is a line bundle of degree $d$ on $C$ and $n$ and $d$ are coprime. It is shown that the universal bundle $\cu_ξ$ on $C\times M_ξ$ is stable with respect to any polarisation on $C\times M_ξ$. It is shown further that the connected component of the moduli space of $\cu_ξ$ containing $\cu_ξ$ is isomorphic to the Jacobian of $C$.

alg-geom↗

arXiv1995

Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve

Let $\MC$ be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree, over a smooth projective curve $C$. This paper identifies the algebraic cohomology ring $\HA^*(\MC)$, i.e. the subring of the rational cohomology ring $H^*(\MC;\QQ)$ spanned by the fundamental classes of algebraic cycles, in terms of the algebraic cohomology ring of the Jacobian $\JC$.

alg-geom↗