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Endomorphisms of symbolic algebraic varieties

Misha Gromov (1999)

Journal of the European Mathematical Society

The theorem of Ax says that any regular selfmapping of a complex algebraic variety is either surjective or non-injective; this property is called surjunctivity and investigated in the present paper in the category of proregular mappings of proalgebraic spaces. We show that such maps are surjunctive if they commute with sufficiently large automorphism groups. Of particular interest is the case of proalgebraic varieties over infinite graphs. The paper intends to bring out relations between model theory,...

Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero

Piedra-Sánchez, R., Tornero, J. (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 14B05, 32S25.The smooth equimultiple locus of embedded algebroid surfaces appears naturally in many resolution processes, both classical and modern. In this paper we explore how it changes by blowing–up.* Supported by FQM 304 and BFM 2000–1523. ** Supported by FQM 218 and BFM 2001–3207.

Estimates of the number of rational mappings from a fixed variety to varieties of general type

Tanya Bandman, Gerd Dethloff (1997)

Annales de l'institut Fourier

First we find effective bounds for the number of dominant rational maps f : X Y between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type { A · K X n } { B · K X n } 2 , where n = dim X , K X is the canonical bundle of X and A , B are some constants, depending only on n .Then we show that for any variety X there exist numbers c ( X ) and C ( X ) with the following properties:For any threefold Y of general type the number of dominant rational maps f : X Y is bounded above by c ( X ) .The number of threefolds Y , modulo birational...

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