A study of variation of mixed Hodge structure (Q1090373)

By an admissible graded polarizable variation of mixed Hodge structure (g.p. VMHS) on a complex space X (on which a smooth Zariski open subset \(X^*\) is given) the author understands a g.p. VMHS whose restriction to any curve meeting \(X^*\) is admissible in the sense of \textit{J. Steenbrink} and \textit{S. Zucker} [Invent. Math. 80, 489-542 (1985)]. A study of admissible g.p. VMHS' is made; especially it is proved that if admissibility holds outside a subspace of codimension 2 of X then it holds on the whole of X (provided X is smooth and \(X\setminus X^*\) is a divisor with normal crossings).