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- W2951423905 abstract "We denote by FPMC the class of all non-singular projective algebraic surfaces X over C with a finite polyhedral Mori cone NE(X)subset NS(X)otimes R. If rho(X)=rk NS(X)ge 3, then the set Exc(X) of all exceptional curves on Xin FPMC is finite and generates NE(X). Let delta_E(X) be the maximum of (-E^2) and p_E(X) the maximum of p_a(E) respectively for Ein Exc(X). For fixed rho ge 3, delta_E and p_E we denote by FPMC_{rho,delta_E,p_E} the class of all Xin FPMC such that rho(X)=rho, delta_E(X)=delta_E and p_E(X)=p_E. We prove that the class FPMC_{rho,delta_E,p_E} is bounded: for any Xin FPMC_{rho,delta_E,p_E} there exist an ample effective divisor h and a very ample divisor h' such that h^2le N(rho,delta_E) and {h'}^2le N'(rho,delta_E,p_E) where the constants N(rho,delta_E)$ and N'(rho,delta_E,p_E) depend only on (rho, delta_E) and (rho, delta_E, p_E) respectively. One can consider Theory of surfaces Xin FPMC as Algebraic Geometry analog of the Theory of arithmetic reflection groups in hyperbolic spaces." @default.
- W2951423905 created "2019-06-27" @default.
- W2951423905 creator A5063293767 @default.
- W2951423905 date "1998-06-09" @default.
- W2951423905 modified "2023-09-27" @default.
- W2951423905 title "A remark on algebraic surfaces with polyhedral Mori cone" @default.
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