Seminar series
Date
Mon, 08 Oct 2012
Time
12:00 -
13:00
Location
L3
Speaker
Philip Candelas
Organisation
Oxford
I will discuss some of the subtleties involved in counting lines on Calabi-Yau threefolds and then discuss the lines on the Dwork pencil of quintic threefolds. It has been known for some time that the manifolds of the pencil contain continuous families of lines and it is known from the work of Angca Mustata that there are 375 discrete lines and also two families parametrized by isomorphic curves that are 125:1 covers of genus six curves $C_{\pm\varphi}$. The surprise is that an explicit parametrization of these families is not as complicated as might have been anticipated. We find, in this way, what should have anticipated from the outset, that the curves $C_\varphi$ are the curves of the Wiman pencil.