The X-method for klt surfaces in positive characteristic

In this paper, we establish a weak version of the Kodaira vanishing theorem for surfaces in positive characteristic. As an application, we obtain some fundamental theorems in the minimal model theory for klt surfaces.Comment: 24 pages, v2:minor revision following referee's comment

Abundance theorem for semi log canonical surfaces in positive characteristic

We prove the abundance theorem for semi log canonical surfaces in positive characteristic.Comment: 33 pages. v2: I added Section 3, changed the definition of slc surfaces, and adopted the one of Kollar. v3: minor change

Boundedness of regular del Pezzo surfaces over imperfect fields

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