January 12 Robert Lazarsfeld (Stony Brook University) |
Measures of irrationality for algebraic varieties |
I'll survey a circle of ideas around the question of measuring "how irrational" are various classes of non-rational varieties. |
January 19 Changho Keem (Seoul National University) |
Hilbert scheme of smooth projective algebraic curves and its irreducibility and rigidity |
Very often in algebraic geometry, the totality of geometric objects under some natural setting becomes again an algebraic variety, which is one the main object of study in algebraic geometry. Hilbert scheme is one of such space parametrizing families of projective algebraic varieties having the same fixed Hilbert polynomial, i.e. sharing certain basic extrinsic attributes and intrinsic invariants. In this talk we will start with the basic construction of the Hilbert scheme of projective algebraic curves due to Alexander Grothendiek. We then proceed further and discuss about the current state of affairs especially on the irreducibility and the rigidity of the Hilbert scheme of smooth projective curves after reviewing a brief history of the study since the era of Italian school. |
February 23 Mark Gross (University of Cambridge) |
A general mirror symmetry construction |
March 9 Brooke Ullery (Harvard University) |
Gonality of complete intersection curves |
The gonality of a smooth projective curve is the smallest degree of a map from the curve to the projective line. If a curve is embedded in projective space, it is natural to ask whether the gonality is related to the embedding. In my talk, I will discuss recent work with James Hotchkiss. Our main result is that, under mild degree hypotheses, the gonality of a complete intersection curve in projective space is computed by projection from a codimension 2 linear space, and any minimal degree branched covering of P^{1} arises in this way. |
Organizers: Elham Izadi, James McKernan and Dragos Oprea
This seminar is supported in part by grants from the NSF. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Past quarters: Fall 2013, Winter 2014, Spring 2014, Fall 2014, Fall 2017. Contact Jonathan Conder at jconder@ucsd.edu about problems with the website or posters.