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Toward moduli of singular varieties. (English) Zbl 0666.14003

Summary: The paper under review is part of the author’s thesis devoted to the study of a problem of the theory of moduli of algebraic varieties. Main result:
Theorem. Let us consider families of polarized varieties \((V,X)\) with fixed Hilbert polynomial. Then the coarse moduli space of moduli of such objects exists as a separable algebraic space of finite type in the following cases:
(i) irregular, normal, non-ruled surfaces;
(ii) non-ruled surfaces with \(q>0\) or with \(p_ g>0\) and only with rational singularities;
(iii) non-ruled surfaces with only minimal singularities;
(iv) irregular, normal, non-uniruled, 3-dimensional varieties with only isolated singularities;
(v) non-uniruled 3-dimensional varieties with only minimal singularities;
(vi) 3-dimensional varieties with \(p_ g>0\) and only rational singularities;
(vii) non-uniruled smooth varieties.

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14J10 Families, moduli, classification: algebraic theory
14J17 Singularities of surfaces or higher-dimensional varieties
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References:

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