Geodesic
On the gluing of germs of complex analytic spaces, Betti numbers, and their structure
Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 582-597

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DOI

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.
DOI : 10.4153/S0008439524000961
Mots-clés : Germs of analytic spaces, gluing of analytic spaces, singularities 
Freitas, Thiago Henrique; Lima, Johnny Albert. On the gluing of germs of complex analytic spaces, Betti numbers, and their structure. Canadian mathematical bulletin, Tome 68 (2025) no. 2, pp. 582-597. doi: 10.4153/S0008439524000961
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     title = {On the gluing of germs of complex analytic spaces, {Betti} numbers, and their structure},
     journal = {Canadian mathematical bulletin},
     pages = {582--597},
     year = {2025},
     volume = {68},
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     doi = {10.4153/S0008439524000961},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000961/}
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