30 citations · 200 across the 41 of their papers we have counts for
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On p-power freeness in positive characteristic
Hiromu Tanaka
In this note, we study base point freeness up to taking p-power, which we will call p-power freeness. We first establish some criteria for p-power freeness as analogues of criteria…
Boundedness of regular del Pezzo surfaces over imperfect fields
Hiromu Tanaka
For a regular del Pezzo surface , we prove that is very ample. Furthermore, we also give an explicit upper bound for the volume which depends only on $[k : k^…
On del Pezzo fibrations in positive characteristic
Fabio Bernasconi, Hiromu Tanaka
We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles…
Invariants of algebraic varieties over imperfect fields
Hiromu Tanaka
We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective o…