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On the gluing of germs of complex analytic spaces, Betti numbers, and their structure

Part of: Singularities Local rings and semilocal rings

Published online by Cambridge University Press:  20 December 2024

Thiago Henrique Freitas Open the ORCID record for Thiago Henrique Freitas [Opens in a new window]  and
Johnny Albert Lima Open the ORCID record for Johnny Albert Lima [Opens in a new window]
Thiago Henrique Freitas
Affiliation:
Department of Mathematics, Universidade Tecnológica Federal do Paraná, 85053-525, Guarapuava-PR, Brazil e-mail: [email protected]
Johnny Albert Lima*
Affiliation:
Department of Mathematics, Universidade Tecnológica Federal do Paraná, 85053-525, Guarapuava-PR, Brazil e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

In this paper, we introduce new classes of gluing of complex analytic space germs, called weakly large, large, and strongly large. We describe their Poincaré series and, as applications, we give numerical criteria to determine when these classes of gluing of germs of complex analytic spaces are smooth, singular, complete intersections and Gorenstein, in terms of their Betti numbers. In particular, we show that the gluing of the same germ of complex analytic space along any subspace is always a singular germ.

Keywords

Germs of analytic spacesgluing of analytic spacessingularities

MSC classification

Primary: 32S05: Local singularities
Secondary: 32S10: Invariants of analytic local rings 13H15: Multiplicity theory and related topics
Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 2 , June 2025 , pp. 582 - 597
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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