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Normal projective surfaces with \(\rho = 1, P_{-1}\geqslant 5\). (English) Zbl 0813.14024

The author, motivated by his previous research concerning the degenerations of the projective plane [see J. Reine Angew. Math. 419, 89- 118 (1991; Zbl 0719.14023)], in the paper under review studies the normal projective surfaces \(X\) with Picard number one and \((-1)\)-genus \(\geq 5\). One of the consequences of the results proved is the following:
Theorem. If \(X\) is a surface as above having at worst rational singularities, then \(X\) has at most one non-cyclic singularity. – Moreover, if \(X\) has only cyclic singularities then \(X\) has at most three singular points.
Further information about the degenerations of the projective plane are also given.

MSC:

14C22 Picard groups
14N05 Projective techniques in algebraic geometry
14J10 Families, moduli, classification: algebraic theory

Citations:

Zbl 0719.14023
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References:

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