Chennai Mathematical Institute


3.30 p.m.
Geometry and Syzygies of Line Bundles on an Algebraic Surface

Krishna Chaitanya
University of Kansas, U.S.A.


The syzygyies of a very ample line bundle $L$ on a projective variety $X \subset \mathbb{P}(H^0(X,L))$ carry information about the geometry of the embedding. This interplay was studied in depth by M. Green and he defined the notion of $N_p$ property for $L$, where $p$ is a natural number. While this situation is fairly well understood for curves, there is no completely satisfactory answer in higher dimensions. I will talk about some new results in this direction for surfaces. This is joint work with B. P. Purnaprajna.