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In this paper we study the existence problem for products in the categories of quasi-projective and algebraic varieties and also in the category of algebraic spaces.
The main result of the paper says that all schematic points of the source of an action of on an algebraic space are schematic on .
After an initial discussion at the Committee of Mathematics Polish Academy of Sciences (CM PAS) meeting in February 2013 concerning the status of Applied Mathematics in Poland, I had a feeling of confusion and dissatisfaction, because it seemed to me, both to define the concepts mentioned by the panelists, like, the more standing problems, there was not sufficiently clear. Taking now the voice I have in the first place to that the slightly harden the soil considerations and, perhaps naively, to...
The aim of this paper is to extend the results of [BB-Ś2] concerning geometric quotients of actions of SL(2) to the case of good quotients. Thus the results of the present paper can be applied to any action of SL(2) on a complete smooth algebraic variety, while the theorems proved in [BB-Ś2] concerned only special situations.
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