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Making conical compactifications wonderful. (English) Zbl 0934.32014

From the introduction: “Let \(M\) be a complex manifold. Assume that \(M\) admits a canonical compactification \(X\) i.e. roughly each point on \(X\) has a neighborhood in which \(X\setminus M\) has a structure of a cone.
In this paper, the authors construct a “minimal wonderful compactification” \(\widetilde X\) of \(M\).
It turns out that several compactifications exhibited earlier [Sel. Math., New Ser. 1, 459-494 (1995; Zbl 0842.14038) Lect. Notes Math. 996, 1-44 (1983; Zbl 0581.14041) and Adv. Stud. Pure Math. 6, 481-513 (1985; Zbl 0596.14041)] are examples of the minimal wonderful compactifications constructed in this paper.

MSC:

32J05 Compactification of analytic spaces
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
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