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Real algebraic threefolds I. Terminal singularities.

János Kollár (1998)

Collectanea Mathematica

The aim of this series of papers is to develop the theory of minimal models for real algebraic threefolds. The ultimate aim is to understand the topology of the set of real points of real algebraic threefolds. We pay special attention to 3–folds which are birational to projective space and, more generally, to 3–folds of Kodaira dimension minus infinity.present work contains the beginning steps of this program. First we classify 3–dimensional terminal singularities over any field of characteristic...

Regular analytic transformations of 2

Joseph Gubeladze (2000)

Annales Polonici Mathematici

Existence of loops for non-injective regular analytic transformations of the real plane is shown. As an application, a criterion for injectivity of a regular analytic transformation of 2 in terms of the Jacobian and the first and second order partial derivatives is obtained. This criterion is new even in the special case of polynomial transformations.

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