#### Alladi Ramakrishnan Hall

#### Stability of Parabolic Poincare bundle

#### Suratno Basu

##### IMSc

*Let X be a smooth, irreducible, projective curve (defined over complex numbers) and S be a finite set of points on X. We denote by M_{\alpha}(\Lambda), the moduli space of rank r at least 2, semi-stable parabolic bundles with complete flags at each point of S and of fixed determinant \Lambda. In this case, it is known that there exists a `Parabolic universal bundle' on X\times M_{\alpha}(\Lambda), with parabolic structure over the divisor S\times M_{\alpha}(\Lambda). In this talk we shall discuss the (slope) stability of these bundles as parabolic bundles. This question was motivated by an earlier work of Balaji, Brambila-Paz and Newstead. We begin with a brief exposition of their work.*

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