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Titlebook: Compact Complex Surfaces; Wolf P. Barth,Klaus Hulek,Antonius Ven Book 2004Latest edition Springer-Verlag Berlin Heidelberg 2004

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書目名稱Compact Complex Surfaces
編輯Wolf P. Barth,Klaus Hulek,Antonius Ven
視頻videohttp://file.papertrans.cn/231/230779/230779.mp4
概述Includes supplementary material:
叢書名稱Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati
圖書封面Titlebook: Compact Complex Surfaces;  Wolf P. Barth,Klaus Hulek,Antonius Ven Book 2004Latest edition Springer-Verlag Berlin Heidelberg 2004
描述In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac- cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider‘s new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom
出版日期Book 2004Latest edition
版次2
doihttps://doi.org/10.1007/978-3-642-57739-0
isbn_softcover978-3-642-57738-3
isbn_ebook978-3-642-57739-0Series ISSN 0071-1136 Series E-ISSN 2197-5655
issn_series 0071-1136
copyrightSpringer-Verlag Berlin Heidelberg 2004
The information of publication is updating

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Examples,ast and very difficult step towards the affirmative answer was done only in the late 1970s by S. - T. Yau. The striking point is that the only known proof uses analysis (hidden in Riemann-Roch for non-algebraic surfaces) and differential geometry as well as the methods of analytic and algebraic geometry.
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Book 2004Latest editiont sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invari
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Mappings of Surfaces, 2 and depends on the fact that one can contract a (?1)-curve, i.e., a smooth rational curve with self intersection ? 1, to a . point. This and its applications to the existence of minimal models is treated in Sect. 4. Curves contractible to (singular) points are treated more generally in Sect. 2.
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The Enriques Kodaira Classification, deduce Castelnuovo’s criterion as a corollary. After all this the classification of minimal algebraic surfaces becomes quite easy. The classification of non-algebraic surfaces which follows next, is the same as in the first edition of the book. In Sect. 8 we prove Iitaka’s results concerning the stability of the ten classes under deformations.
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