Effective non-vanishing for algebraic surfaces in positive characteristic
The author proves a few non-vanishing theorems on algebraic surfaces defined over a field of positive characteristic. These are sort of the generalizations to the original conjectures of Ambro, Kawamata et al. The original non-vanishing problem in the zero characteristic case was solved by \textit{Y. Kawamata} [Asian J. Math. 4, No.~1, 173--181 (2000; Zbl 1060.14505)] provided the variety is a surface or is a minimal threefold. There is also a generalization of Kawamata's conjecture / result to the \(\mathbb Q\)-divisors on surfaces by \textit{J. A. Chen, M. Chen} and the reviewer [J. Algebra 293, 363--384 (2005; Zbl 1093.14010)]. The author also gives examples on ruled surfaces to show that Kawamata-Viehweg vanishing or Kollar vanishing may not hold when the characteristic is positive.
scientific article