Recent zbMATH articles in MSC 14-03https://zbmath.org/atom/cc/14-032024-03-13T18:33:02.981707ZWerkzeugOn the splitting principle of Beniamino Segrehttps://zbmath.org/1528.140142024-03-13T18:33:02.981707Z"Felisetti, Camilla"https://zbmath.org/authors/?q=ai:felisetti.camilla"Fontanari, Claudio"https://zbmath.org/authors/?q=ai:fontanari.claudioIn the paper under review, the authors prove a stronger version of the classical principle of connectedness saying that if the general member \(X_t\) of a flat family \(X \to T\) over an irreducible curve of finite type is connected, then \(X_t\) is connected for all \(t \in T\).
The authors present with the language of modern algebraic geometry a result about the irreducibility of fibers of a flat family of nodal curves lying on a smooth surface. The result was firstly claimed by \textit{B. Segre} [Ann. Mat. Pura Appl. (4) 17, 107--126 (1938; Zbl 0019.07901; JFM 64.0688.02)].
Reviewer: Paolo Lella (Trento)