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 $[k:k^p]$ for the base field $k$. As a consequence, we obtain the boundedness of geometrically integral regular del Pezzo surfaces.

24 pages, v2: minor revisions, v3: minor revisions, v4: minor revisions

References in corpus (2)

• On del Pezzo fibrations in positive characteristic
• Invariants of algebraic varieties over imperfect fields

Cited by in corpus (1)

• Invariants of algebraic varieties over imperfect fields