Boundedness of regular del Pezzo surfaces over imperfect fields

Abstract

For a regular del Pezzo surface $X$, we prove that $|-12K_X|$ is very ample. Furthermore, we also give an explicit upper bound for the volume $K_X^2$ which depends only on its thickening exponent $\epsilon(X/k)$. As a consequence, we obtain the boundedness of geometrically integral regular del Pezzo surfaces.Comment: 27 page