2 citations · 2 across the 4 of their papers we have counts for
5 papers
Note on asymptotic behaviour of the canonical ring
Xiaojun Wu
The theory of the Oukounkov body is a useful tool for studying the asymptotic behaviour of the canonical ring of a line bundle over a projective manifold. In this note, combined wi…
On a vanishing theorem due to Bogomolov
Xiaojun Wu
In this note, we give a new proof of a vanishing result originally due to Bogomolov, and later generalised by Mourougane and Boucksom. The statement holds for arbitrary pseudoeffec…
On Junyan Cao's vanishing theorem for pseudoeffective line bundles
Xiaojun Wu
Junyan Cao has obtained a very general vanishing theorem, valid on any compact Kähler manifold, for the cohomology groups with values in a pseudoeffective line bundle twisted by th…
On the Nakano vanishing theorem
Xiaojun Wu
In this note, we state various generalisations of the Nakano vanishing theorem under weak positivity assumptions, and compare them with the known results.
On the hard Lefschetz theorem for pseudoeffective line bundles
Xiaojun Wu
In this note, we obtain a number of results related to the hard Lefschetz theorem for pseudoeffective line bundles, due to Demailly, Peternell and Schneider. Our first result state…