Plurigenera of Surface SingularitiesNova Science Publishers, 2000 - 98 pagine The aim of this book is to introduce the plurigenera of isolated singularities of normal complex analytic spaces. Though there are three kinds of typical plurigenera {???}, {???} and {???}, most of the results in this book are related to the L(2)-plurigenera ???. |
Sommario
Basic facts on surface singularities | 23 |
Csurface singularities | 47 |
Polynomial periodicity | 59 |
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Parole e frasi comuni
A₁ assertion follows b₁ b₂ blowing-up Bois singularity C*-surface singularity canonical divisor coherent sheaf complex analytic space Corollary cusp singularity cyclic quotient singularity d₁ d₂ deformation of X,x denote dimc elliptic or cusp equisingular deformation exact sequence exists a unique f-nef finite follows from Theorem formula function fundamental cycle Gorenstein singularity graph of X,x Hence we obtain homomorphism hypersurface hypersurface singularity intersection matrix invertible sheaf irreducible components Ishii isolated singularity isomorphic Laufer Lemma Let f Let X,x log-canonical singularity Math minimal good resolution minimal resolution minimally elliptic singularity morphism nonsingular nonsingular rational curves Nred Ox(mKx plurigenera positive cycle positive integer PROOF Proposition Q-cycle rational curves rational double point rational singularity resp Riemann-Roch theorem Serre duality simple elliptic Sing(X star-shaped graph strict transform subset Suppose that X,x surface singularity X,x surjective versal deformation w₁ Wahl Watanabe 97 weighted dual graph Zariski decomposition