Definition of a Singularity, Resolutions of Singularities

Shihoko Ishii
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Shihoko Ishii: The University of Tokyo, Graduate School of Mathematical Sciences

Chapter Chapter 4 in Introduction to Singularities, 2014, pp 55-80 from Springer

Abstract: Abstract In this chapter we define singularities on analytic spaces or on algebraic varieties. Then, we introduce the fact that an isolated singularity on an analytic space can be regarded as a singularity on an algebraic variety. We also introduce Hironaka’s theorem stating that every algebraic variety over a field of characteristic zero has a resolution of the singularities. In this book our interest is focused on singularities. To this end, we study the resolved space instead of studying the singularity itself, therefore this resolution theorem is essential.

Keywords: Algebraic Varieties; Resolved Space; Resolution Theorem; Space Analysis; Finite Fan (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-55081-5_4

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DOI: 10.1007/978-4-431-55081-5_4

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