A1A1 curves on quasi-projective varieties - Qile Chen
Qile Chen Columbia University March 17, 2015 In this talk, I will present the recent joint work with Yi Zhu on A1A1-connectedness for quasi-projective varieties. The theory of A1A1-connectedness for quasi-projective varieties is an analogue of rationally connectedness for projective varieties. To study curves on a quasi-projective variety UU, we compactify UU by a log smooth pair (X,D)(X,D). Using the theory of stable log maps to (X,D)(X,D), we were able to produce A1A1 curves on UU from degeneration. This provides many interesting examples of A1A1-connected varieties. Some applications to arithmetic geometry and usual rationally connectedness will be discussed as well. More videos on http://video.ias.edu
Qile Chen Columbia University March 17, 2015 In this talk, I will present the recent joint work with Yi Zhu on A1A1-connectedness for quasi-projective varieties. The theory of A1A1-connectedness for quasi-projective varieties is an analogue of rationally connectedness for projective varieties. To study curves on a quasi-projective variety UU, we compactify UU by a log smooth pair (X,D)(X,D). Using the theory of stable log maps to (X,D)(X,D), we were able to produce A1A1 curves on UU from degeneration. This provides many interesting examples of A1A1-connected varieties. Some applications to arithmetic geometry and usual rationally connectedness will be discussed as well. More videos on http://video.ias.edu