The Demailly systems with the Vortex ansatz

For an arbitrary-rank vector bundle over a projective manifold, J.-P. Demailly proposed several systems of equations of Hermitian-Yang-Mills type for the curvature tensor to settle a conjecture of Griffiths on the equivalence of Hartshorne ampleness and Griffiths positivity. In this article, we have studied two proposed systems and proved that these equations have smooth solutions for the Vortex bundle using the continuity method.Comment: 21 page

The Indian Stock Market and the Great Recession

This study analyzes the impact of the outbreak of the Great Recession of 2007 on the behavior of the Indian stock market. The SENSEX index of the Bombay Stock Exchange is analyzed for the prerecession period of January 2002 – November 2007 and the postrecession outbreak period of December 2007 – July 2010. Substantial increase in SENSEX return volatility observed during the post-recession outbreak period, whereas no substantial difference in returns between two periods is found. Also strong co-movements in returns and volatility are observed between the SENSEX and other major stock indexes during the post-recession period. Our results establish the dominance of global factors in influencing Indian stock market behavior during periods of economic turmoil