Chennai Mathematical Institute


On the geometry of surfaces of general type
Prof. B.P. Purnaprajna
University of Kansas, U.S.A.


The Canonical map (that is the map induced by the canonical linear series) of an algebraic curve $C$ of genus $g>1$ is reasonably well understood: either it is an embedding or maps $C$ 2:1 onto a rational normal curve. For an algebraic variety of dimension two or higher, the canonical map is much more subtle due to, among other things, the existence of higher degree covers. I will talk about some results (with F. J. Gallego) on the canonical map of a surface of general type and its connection to various aspects of the geometry of these varieties including the so-called ``mapping geography'' of surfaces of general type, ring generation of the canonical ring, fundamental groups, Kahler geometric aspects and linear series on threeefolds such as Calabi-Yau.