Stability of homogeneous bundles on P^3

We study the stability of some homogeneous bundles on P^3 by using their representations of the quiver associated to the homgeneous bundles on P^3. In particular we show that homogeneous bundles on P^3 whose support of the quiver representation is a parallelepiped are stable, for instance the bundles E whose minimal free resolution is of the kind 0 --> S^{l_1, l_2, l_3} V (t) --> S^{l_1 +s, l_2, l_3} V (t+s) --> E --> 0 are stable.Comment: to appear in Geometriae Dedicata http://www.springer.com/mathematics/geometry/journal/1071

On faltings parabolic theta functions

In this article, we prove that the Faltings theta functions on moduli of parabolic bundles over a smooth projective curve can be used to give an explicit scheme-theoretic projective embedding.by Sanjay Amrutiy