The Real Story of Linear Series on P1

Frank Sottile
University of Masssachusetts, Amherst
Columbia University 7 November 2003

    Real algebraic geometry is a difficult subject. Basic questions about some of the most elementary objects may not have answers that seem satisfactory when compared to the answers obtained in classical algebraic geometry. Nevertheless, it is a well-developed subject and an important one as applications demand real solutions. There are also many hidden gems in the subject.

    This talk will try to illustrate these remarks in a corner of the subject that I know well---real linear series on P1. For a preview of some of the talk, below are pictures of linear series on P1 of dimension 3 and degree 4 with simple real ramification.


These curves, statically.
For a more complete story on these curves, go here.
For conjectures concerning linear series on P1, try this.