Monads on a Multiprojective Space, P× P b

Abstract

For all integers a, b > 0 we establish explicitly the existence of monads on a multiprojective Space Pa×Pb following the conditions established by Floystad. That is for all positive integers α, β, γ there exists a monad on the multiprojective space X = Pa × Pb whose maps A and B have entries being linear in two sets of homogeneous coordinates x0 : ... : xa and y0 : ... : yb and it takes the form: 0 Oα X(−1,−1)A Oβ X B Oγ X(1, 1) 0 where the maps A and B are matrices with B ·A = 0 and they are of maximal rank.