Real algebraic threefolds. I: Terminal singularities (Q1817873)

This is the first of a series of papers in which the author develops the theory of the minimal models of real algebraic threefolds. The minimal model program for complex algebraic varieties [see e.g. \textit{J. Kollár}, Bull. Am. Math. Soc., New Ser. 17, 211-273 (1987; Zbl 0649.14022)] shows in particular that the minimal models \(X_n\) of smooth projective complex varieties \(X\) can be non-smooth, but also that \(X_n\) may have at most terminal singularities. The terminal 3-fold singularities over \({\mathbb C}\) are completely classified [see e.g. \textit{M. Reid}, in: Algebraic Geometry, Proc. Summer Res. Inst., Brunswick 1985, Part I, Proc. Symp. Pure Math. 46, 345-414 (1987; Zbl 0634.14003)]. In the present work are classified the 3-fold terminal singularities over any field \(k\) of characteristic \(0\). When \(k\) is the field of real numbers then the obtained classification is used to determine the topology of these singularities over \({\mathbb R}\).