000			02655nam a22003497a 4500
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020			_a9783540586630
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a512.7 _bHIR-T
100			_aHirzebruch, Friedrich
245			_aTopological methods in algebraic geometry
260			_aNew York : _bSpringer- Verlag, _c1995.
300			_aix, 234p. ; _c24 cm.
490			_aClassics in mathematics _x1431-0821
504			_aIncludes bibliographical references (p. [218]-225) and index.
520			_aIn recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for­ mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo­ morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954.
650		0	_aGeometry, Algebraic.
650		0	_aAlgebraic topology.
650			_aRiemann-Roch theorem
650			_aAlgebraic varieties
650			_aCohomology
650			_aVector bundle
650			_aCorbordism ring
650			_aHomology
650			_aTodd genus
650			_aTopological methods
856			_uhttps://link.springer.com/book/10.1007/978-3-642-62018-8#toc _3Table of contents
856			_uhttps://www.goodreads.com/book/show/2585236-topological-methods-in-algebraic-geometry?from_search=true&from_srp=true&qid=xU8dcxz1Fy&rank=1#CommunityReviews _3Reviews
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