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Buchdahl, Nicholas

Algebraic deformations of compact Kähler surfaces. (English) Zbl 1118.32016

Math. Z. 253, No. 3, 453-459 (2006).
The author proves a weakened version of K. Kodaira’s result [Ann. Math. (2) 78, 1–40 (1963; Zbl 0171.19601)] namely: Theorem. A non-algebraic compact Kähler surface \(X\) with \(H^2(X,\Theta_X)= 0\) has arbitrarily small deformations which are algebraic.
The proof makes no essentially no reference to the classification of surfaces.
Reviewer: Viorel Vâjâitu (Bucureşti)

Cited in 1 Review
Cited in 9 Documents

MSC:

32J15 Compact complex surfaces
53C55 Global differential geometry of Hermitian and Kählerian manifolds
14J10 Families, moduli, classification: algebraic theory

Keywords:

compact Kähler surface; algebraic surface; deformation

Citations:

Zbl 0171.19601
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\textit{N. Buchdahl}, Math. Z. 253, No. 3, 453--459 (2006; Zbl 1118.32016)
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References:

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