author

会議発表論文

会議発表論文

text

Commutative Algebra, Algebraic Geometry, and Computational Methods P.135-P.144

Recovery of Vanishing Cycles by Log Geometry : Case of Several Variables

Usui, Sampei

臼井, 三平

Springer

英語

1999

http://hdl.handle.net/11094/73420

a proceeding of International Conference "Commutative Algebra and Algebraic Geometry and Computational Methods", Hanoi 1996

This article is a generalization of the author's work [U] to the case of several variables. We first construct compatible actions of monoid S on a “several-variables- version of semi-stable degeneration of pairs” and on the associated log topological spaces introduced by K. Kato and C. Nakayama in [KN]. Here S is the product of the unit interval and the unit circle. Then we show that the associated log topological family is locally piecewise C^∞ trivial over the base, i.e., the associated log topological family recovers the vanishing cycles, in the most naive sense, of the original degeneration. Using this result together with the theory of canonical extensions by Deligne [D], we introduce two types of integral structure of the variation of mixed Hodge structure associated to “several-variables-version of semi-stable degeneration of pairs”. We only sketch the proof here. The complete proof will appear soon somewhere.

Recovery of Vanishing Cycles by Log Geometry : Case of Several Variables

Usui, Sampei

Springer

英語

1999

Commutative Algebra, Algebraic Geometry, and Computational Methods

135

144

http://hdl.handle.net/11094/73420