19,405 research outputs found
Comments on Takahashi-Tanimoto's scalar solution
We study the identity-based solution of Witten's cubic bosonic open string
field theory constructed by Takahashi and Tanimoto, which is claimed to
describe the tachyon vacuum. We argue that the observables of the solution
coincide with those of the tachyon vacuum using the method proposed by
Kishimoto and Takahashi. We also discuss how to treat the kinetic term of the
string field theory expanded around it.Comment: 25 pages, 4 figures, v3: several clarifications added, corrected
statements about operator U, v4: comments on operator U_k are adde
Freeness of adjoint linear systems on threefolds with terminal Gorenstein singularities or some quotient singularities
We generalize the result of Kawamata concerning the strong version of
Fujita's freeness conjecture for smooth 3-folds to some singular cases, namely,
Gorenstein terminal singularities and quotient singularities of type 1/r(1,1,1)
and of type 1/r(1,1,-1). We generalize furthermore the result of that to
projective threefolds with only canonical singularities for canonical and not
terminal singularities. It turns out that the estimates in the first three
cases are better than the one for the smooth case, which it is not in the
fourth case. We also give explicit examples which show the estimate in the
fourth case is necessarily worse than the one for the smooth case.Comment: 21 pages, Late
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