Rational curves in the log category
Rational curves in the log category

Yi Zhu, University of Utah
Fine Hall 322
In birational geometry, log pairs are introduced for studying open varieties and for reducing problems to lower dimensional case. In this talk, I will explain that this framework can be used to study rational curves on varieties. I will introduce A^1connectedness for log smooth pairs, i.e., the interior admits lots of rational curves which meet the boundary once. A typical example is a projective space with a smooth Fano hypersurface. Then I will discuss several joint works with Qile Chen as applications of A^1connected varieties. One application gives a simple proof of general Fano complete intersections are separably rationally connected.