抄録
In [12] Ishida introduces a complex, denoted by $¥tilde {¥Omega}^{^.}_Y$, associated to a filtered semi-toroidal variety Y over Spec C and proves that it is quasi-isomorphic to the Du Bois complex $¥underline{¥underline{¥Omega}}^{^.}_Y$ ([5]). In this article we regard a filtered semi-toroidal variety Y as an ideally log smooth log scheme over Spec C, and we give an interpretation of the Ishida complex $¥tilde{¥Omega}^{^.}_Y$ in terms of logarithmic geometry. Therefore, given a log smooth log scheme X over Spec C, we use this logarithmic interpretation of the Ishida complex to construct the following distinguished triangle in the Du Bois derived category Ddiff (X): IMω.X → $¥tilde{¥Omega}^{^.}_X$ → $¥tilde{¥Omega}^{^.}_D$ → ·, where D = X – Xtriv (Xtriv being the trivial locus for the log structure M on X). Since the complex IMω.X calculates the De Rham cohomology with compact supports of the smooth analytic space $X_{triv}^{an}$ ([20, Corollary 1.6]), this triangle is useful to give an interpretation of H.DR,c(Xtriv/C) as the hyper-cohomology of the simple complex $¥underline{¥underline{s}}[¥underline{¥underline{¥Omega}}^{^.}_X ¥longrightarrow ¥underline{¥underline{¥Omega}}^{^.}_D]$.
