Algebraic dimension of twistor spaces whose fundamental system is a pencil

作者：Honda Nobuhiro^*; Kreussler Bernd

来源：Journal of the London Mathematical Society-Second Series, 2017, 95(3): 989-1010.

DOI：10.1112/jlms.12043

We show that the algebraic dimension of a twistor space over nCP(2) cannot be two if n > 4 and the fundamental system (that is, the linear system associated to the half-anti-canonical bundle, which is available on any twistor space) is a pencil. This means that if the algebraic dimension of a twistor space on nCP(2), n > 4, is two, then the fundamental system is either empty or consists of a single member. The existence problem for a twistor space on nCP2 with algebraic dimension two is open for n > 4.

• 出版日期2017-6