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

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  • Thiago Henrique Freitas, Johnny Albert Lima
  • Journal:
    Canadian Mathematical Bulletin , First View
    Published online by Cambridge University Press:
    20 December 2024, pp. 1-16
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  • 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.