On the geometry of surfaces of general type
Prof. B.P. Purnaprajna
University of Kansas, U.S.A.
26-04-06

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Abstract

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.