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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...

Effective Nullstellensatz for arbitrary ideals

János Kollár — 1999

Journal of the European Mathematical Society

Let f i be polynomials in n variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials g i such that g i f i = 1 . The effective versions of this result bound the degrees of the g i in terms of the degrees of the f j . The aim of this paper is to generalize this to the case when the f i are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.

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