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A remark on algebraic surfaces with polyhedral Mori cone
| Content Provider | Scilit |
|---|---|
| Author | Nikulin, Viacheslav V. |
| Copyright Year | 2000 |
| Description | 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. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/DB47DDDD1BBDC293924D4B001D8C40CD/S0027763000007194a.pdf/div-class-title-a-remark-on-algebraic-surfaces-with-polyhedral-mori-cone-div.pdf |
| Ending Page | 92 |
| Page Count | 20 |
| Starting Page | 73 |
| ISSN | 00277630 |
| e-ISSN | 21526842 |
| DOI | 10.1017/s0027763000007194 |
| Journal | Nagoya Mathematical Journal |
| Volume Number | 157 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2000-01-01 |
| Access Restriction | Open |
| Subject Keyword | Nagoya Mathematical Journal Applied Mathematics Surfaces X |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
