Assadi A, Barlow R, Knop F (1992)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1992
Publisher: Springer Verlag (Germany)
Book Volume: 210
Pages Range: 129-136
Journal Issue: 1
DOI: 10.1007/BF02571787
Theorem: Let X be a complete algebraic variety over an algebraically closed field of characteristic p>=0, and let G be a finite abelian group acting on X. Assume the order of G is l^r, where l is a prime different from p. If the fixed point set consists of exactly one point x, then X is singular in X.
Corollary: If X is smooth then G has either no fixed point or at least two of them.
This is an algebraic analogue of (much deeper) results of Conner-Floyd, Atiyah-Bott and others in the topological category.
APA:
Assadi, A., Barlow, R., & Knop, F. (1992). Abelian group actions on algebraic varieties with one fixed point. Mathematische Zeitschrift, 210(1), 129-136. https://doi.org/10.1007/BF02571787
MLA:
Assadi, Amir, Rebecca Barlow, and Friedrich Knop. "Abelian group actions on algebraic varieties with one fixed point." Mathematische Zeitschrift 210.1 (1992): 129-136.
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