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Hilbert-Samuel Multiplicity and Finite Projections

In: Handbook of Geometry and Topology of Singularities IV

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ana Bravo & Santiago Encinas, 2023. "Hilbert-Samuel Multiplicity and Finite Projections," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities IV, chapter 0, pages 521-557, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-31925-9_11
    DOI: 10.1007/978-3-031-31925-9_11
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