GENERIC POINTS IN ALGEBRAIC GEOMETRY AND LOEB MEASURES

Li Banghe

Journal of Systems Science & Complexity ›› 1989, Vol. 2 ›› Issue (1) : 1-003.

PDF(156 KB)
PDF(156 KB)
Journal of Systems Science & Complexity ›› 1989, Vol. 2 ›› Issue (1) : 1-003.
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GENERIC POINTS IN ALGEBRAIC GEOMETRY AND LOEB MEASURES

  • Li Banghe
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Abstract

For any irreducible complex projective variety A, we prove that in the nonstandard extension ~*A of A in a polysaturated model, the set of points which are not generic points of A has Loeb measure zero. This is similar to the Sard theorem asserting that the critical values of a smooth maphave Lebesgue measure zero.

Key words

generic point / Loeb measure

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Li Banghe. GENERIC POINTS IN ALGEBRAIC GEOMETRY AND LOEB MEASURES. Journal of Systems Science and Complexity, 1989, 2(1): 1-003
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