nLab hyperbolic curves

Let kk be an algebraically closed field. Let XX be a smooth one-dimensional variety over kk. Such a curve has a unique projective model X¯\overline X, and X=X¯{x 1,,x r}X=\overline X\smallsetminus \{x_1,\dots,x_r\} for some finite collection x 1,,x rx_1,\dots,x_r of points in X¯\overline X. Let gg be the genus of X¯\overline X. We say that XX is hyperbolic if 2g2+r>02 g-2+r \gt 01.

Last revised on May 31, 2018 at 12:24:11. See the history of this page for a list of all contributions to it.