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.


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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