Titlebook: Algebraic Surfaces; Lucian B?descu Textbook 2001 Springer-Verlag New York 2001 Dimension.Divisor.Grad.Grothendieck topology.algebra.algebr

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Morphisms from a Surface to a Curve. Elliptic and Quasielliptic Fibrations,Let .: . → . be .*: k(.) → k(.) . k(.) . k(.). Then . V ? Y ..(.) ..

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Canonical Dimension of an Elliptic or Quasielliptic Fibration,Let .: . → . be an elliptic or quasielliptic fibration. Theorem 7.15 expresses the dualizing sheaf ω. of . in the form

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Ruled Surfaces. The Noether-Tsen Criterion,A surface . is a . if there exists a nonsingular projective curve . such that . is birationally isomorphic to P. × ..

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Zariski Decomposition and Applications,In this chapter we present Zariski’s theory of finite generation of the graded algebra . (., .) associated to a divisor . on a surface ., cf. [Zar1] and some more recent developments related to this theory.

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978-1-4419-3149-8Springer-Verlag New York 2001

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Murray Gerstenhaber,Samuel D. Schack let .: . → . be its canonical projection. Let . ∈ . be a closed point on the fiber .. = ..(.), . = . (.), and let .be the quadratic transformation of . with center .. Then the proper transform F′ of .. on .has ..(F′) = 0 and (F′.) = ?1, because ..(Fb) = 0 and (F..) = 0. In other words, F′ is an exc

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Minimal Models of Ruled Surfaces, let .: . → . be its canonical projection. Let . ∈ . be a closed point on the fiber .. = ..(.), . = . (.), and let .be the quadratic transformation of . with center .. Then the proper transform F′ of .. on .has ..(F′) = 0 and (F′.) = ?1, because ..(Fb) = 0 and (F..) = 0. In other words, F′ is an exc