Hilbert-Samuel Multiplicity and Finite Projections

Ana Bravo () and Santiago Encinas ()
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Ana Bravo: Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Depto. Matemáticas, Facultad de Ciencias
Santiago Encinas: Instituto de Matemáticas, Universidad de Valladolid, Depto. Álgebra, Análisis Matemático, Geometría y Topología, and IMUVA

Chapter Chapter 11 in Handbook of Geometry and Topology of Singularities IV, 2023, pp 521-557 from Springer

Abstract: Abstract In this (mainly) expository notes, we study the multiplicity of a local Noetherian ring ( B , 𝔪 ) $$(B,{\mathfrak m})$$ at an 𝔪 $${\mathfrak m}$$ -primary ideal I, paying special attention to the geometrical aspects of this notion. To this end, we will be considering suitably defined finite extensions S ⊂ B $$S\subset B$$ , with S regular. We will explore some applications like the explicit description of the equimultiple locus of an equidimensional variety, or the computation of the asymptotic Samuel function.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-31925-9_11

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DOI: 10.1007/978-3-031-31925-9_11

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