Minimal models and abundance for positive characteristic log surfaces

Abstract

We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for Q-factorial surfaces and for log canonical surfaces. Moreover, in the case where the base field is the algebraic closure of a finite field, we obtain the same results under much weaker assumptions.

65 pages; v2: minor revision; v3: I fixed the proof of 9.4; v4: the numbering of theorems were largely changed from v3

Cited by in corpus (2)

• On the three dimensional minimal model program in positive characteristic
• On base point free theorem for log canonical threefolds over the algebraic closure of a finite field