Algebraic dimension of twistor spaces whose fundamental system is a pencil (pre-published version)

2018-10-092018-10-092017Honda, N.; Kreussler, B. (2017) 'Algebraic dimension of twistor spaces whose fundamental system is a pencil'. Journal of the London Mathematical Society 95(3), pp. 989-1010. DOI: 10.1112/jlms.12043http://hdl.handle.net/10395/2236Algebraic dimension of twistor spaces whose fundamental system is a pencilWe show that the algebraic dimension of a twistor space over nℂℙ2 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 nℂℙ2, 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.enghttps://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12043AlgebraTwistor spacesSystemPencilAlgebraic dimension of twistor spaces whose fundamental system is a pencil (pre-published version)Article10.1112/jlms.12043