代数曲面和全纯向量丛

图书信息

分类：科学技术,自然科学,数学

作者简介

作者简介 暂缺《代数曲面和全纯向量丛》作者简介

内容简介

内容简介 暂缺《代数曲面和全纯向量丛》简介

目录

图书目录
PrefaceIntroduction1 Curves on a SurfaceIntroductionInvariants of a surfaceDivisors on a surfaceAdjunetion and arithmetic genusThe Riemann-Roch formulaAlgebraic proof of the Hodge index theoremAmple and nef divisorsExercises2 Coherent SheavesWhat is a coherent sheaf?A rapid review of Chern classes for projective varietiesRank 2 bundles and sub-line bundlesElementary modificationsSingularities of coherent sheavesTorsion free and reflexive sheavesDouble coversAppendix： some commutative algebraExercises3 B|ratlonal GeometryBlowing upThe Castelnuovo criterion and factorization of birationa] morphismsMinimal modelsMore general contractionsExercises4 StabilityDefinition of Mumford-Takemoto stabilityExamples for curvesSome examples of stable bundles on p2Gieseker stabilityUnstable and semlstable sheavesChange of polarizationThe differential geometry of stable vector bundlesExercises5 Some Examples of SurfacesRational ruled surfacesGeneral ruled surfacesLinear systems of cubicsAn introduction to K3 surfacesExercises6 Vector Bundles over Ruled SurfacesSuitable ample divisorsRuled sur facesA brief introduction to local and global moduliA Zariski open subeet of the moduli spaceExercises7 An Introduction to Elliptic SurfacesSingular fibersSingulex fibers of elliptic fibrationslnvariants and the canonical bundle formulaElliptic surfaces with a section and Weierstrass modelsMore general elliptic surfacesThe fundamental groupExercises8 Vector Bundles over Elliptic SurfacesStable bundles on singular curvesStable bundles of odd fiber degree over elliptie surface*A Zariski open subset of the modnii spaceAn overview of Donaldson invariantsThe 2-dimensional invariant……9 Bogomolov's Inequality and Applications10 Classification of Algebraic Surfaces and of Stable BundlesReferencesIndex