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- W1878962550 abstract "We denote by FPMC the class of all non-singular projective algebraic surfaces X over ℂ with finite polyhedral Mori cone NE( X ) ⊂ NS( X ) ⊗ ℝ. If ρ(X ) = rk NS(X) ≥ 3, then the set Exc( X ) of all exceptional curves on X ∈ FPMC is finite and generates NE( X ). Let δ E (X ) be the maximum of (- C 2 ) and pE(X ) the maximum of p a (C ) respectively for all C ∈ Exc( X ). For fixed ρ ≥ 3, δE and p E we denote by FPMC ρ,δE,pE the class of all algebraic surfaces X ∈ FPMC such that ρ(X ) = ρ, δ E (X ) = δ E and p E (X ) = p E . We prove that the class FPMC ρ,δE,pE is bounded in the following sense: for any X ∈ FPMC ρ,δE,pE there exist an ample effective divisor h and a very ample divisor h ′ such that h 2 ≤ N(ρ, δE ) and h ′ 2 ≤ N ′( ρ, δE, pE ) where the constants N(ρ, δE ) and N ′( ρ, δE, pE ) depend only on ρ, δE and ρ, δE, pE respectively. One can consider Theory of surfaces X ∈ FPMC as Algebraic Geometry analog of the Theory of arithmetic reflection groups in hyperbolic spaces." @default.
- W1878962550 created "2016-06-24" @default.
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- W1878962550 date "2000-01-01" @default.
- W1878962550 modified "2023-09-27" @default.
- W1878962550 title "A remark on algebraic surfaces with polyhedral Mori cone" @default.
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- W1878962550 doi "https://doi.org/10.1017/s0027763000007194" @default.
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