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Some combinatorial remarks on normal flatness in analytic spaces

 

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Author: Soto Prieto, Manuel Jesús
Tornero Sánchez, José María
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2014-06
Published in: Taiwanese Journal of Mathematics, 18 (3), 943-971.
Document type: Article
Abstract: In this article we present a combinatorial treatment of normal flatness in analytic spaces, using the idea of equimultiple standard bases. We will prove, using purely combinatorial methods, a characterization theorem for normal flatness. This will lead us to a new proof of a classical theorem on normal flatness, which can be stated by saying that normal flatness at a point along a smooth subspace is equivalent to the Hilbert function being locally constant. Though these topics belong to classical analytic geometry, we believe that this approach is valuable, since it replaces extremely general algebraic theorems by combinatorial objects, obtaining new results and striking the combinatorial nature of the classical (and basic) ideas in the resolution of singularities.
Cite: Soto Prieto, M.J. y Tornero Sánchez, J.M. (2014). Some combinatorial remarks on normal flatness in analytic spaces. Taiwanese Journal of Mathematics, 18 (3), 943-971.
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Format: PDF

URI: http://hdl.handle.net/11441/47579

DOI: 10.11650/tjm.18.2014.3306

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