Titlebook: Resolution of Singularities; A research textbook Herwig Hauser,Joseph Lipman,Adolfo Quirós Textbook 2000 Springer Basel AG 2000 Algebraisc

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Debrief

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Toric Varieties and Toric Resolutionsn toric geometry, including fans, support functions, and ampleness criteria. The paper also explores alternate constructions of toric varieties and nonnormal toric varieties. Then we turn our attention to singularities. We will discuss blowing-up in the toric context and resolution of singularities

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商谈

Culpable

Resolving Singularities of Plane Analytic Branches with one Toric Morphismre . is the number of Puiseux exponents of (., 0). We show, using the specialization of (. 0) to (.., 0), that the same toric morphisms .Σ→ℂ. which induce an embedded resolution of singularities of (.., 0) also resolve the singularities of (., 0) ⊂ (⊂ ℂ., 0), the embedding being defined by elements

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Excellent Surfaces and Their Taut Resolutiondded in three-space and defined over an algebraically closed field of arbitrary characteristic. The proof of strong embedded resolution we describe here combines arguments and techniques of O. Zariski, H. Hironaka, S. Abhyankar and the author.

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Equisingularity and Simultaneous Resolution of Singularitiesans of a generic local projection to affine .-space. A possibly more intuitive concept of equisingularity can be based on stratification by simultaneous resolvability of singularities. The two approaches are known to be equivalent for families of plane curve singularities. In higher dimension we ask

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