4:00 am Thursday, September 9, 2010
Colloquium : Conics on the Fermat quintic threefold
by Damiano Testa (University of Oxford) in HB 227
Many interesting features of algebraic varieties are encoded in the spaces of rational curves that they contain. For instance, a smooth cubic surface in complex projective three-dimensional space contains exactly 27 lines; exploiting the configuration of these lines it is possible to find a (rational) parameterization of the points of the cubic by the points in the complex projective plane. After a general overview, we focus on the Fermat quintic threefold $X$, namely the hypersurface in four-dimensional projective space with equation $x^5+y^5+z^5+u^5+v^5=0$. The space of lines on $X$ is well-known. I will explain how to use a mix of algebraic geometry, number theory and computer-assisted calculations to study the space of conics on $X$. This talk is based on joint work with R. Heath-Brown. Host Department: Rice University-Mathematics
Submitted by dani@rice.edu |
