Topological Methods in Algebraic Geometry (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 131) Second, Corrected Printing of the Third Edition (English and German Edition)

Science & Math

Hirzebruch, Friedrich

Mathematics

Springer

Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations.

Prospects in Mathematics (Annals of Mathematics Studies)

Princeton University Press

The present volume contains Friedrich Hirzebruch's works from 1987 until 2012. It is the continuation of the two volumes "Friedrich Hirzebruch, Gesammelte Abhandlungen", published by Springer-Verlag in 1987. The volume, edited by Joachim Schwermer, Silke Wimmer-Zagier and Don Zagier, includes all of Friedrich Hirzebruch's mathematical publications from this period as well as two lecture reports written by him. These are supplemented by a number of articles and addresses containing historical or biographical material, as well as obituaries or appreciations of people who were mathematically or personally close to him.

Gesammelte Abhandlungen - Collected Papers III: 1988 - 2012

In 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.

Topological Methods in Algebraic Geometry: Reprint of the 1978 Edition (Classics in Mathematics)

Hirzebruch, F.

Friedrich Hirzebruch (1927 –2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure of his generation. Hirzebruch’s first great mathematical achievement was the proof, in 1954, of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem. He received many awards and honors, including the Wolf prize in 1988, the Lobachevsky prize in 1990, and fifteen honorary doctorates. These two volumes collect the majority of his research papers, which cover a variety of topics.

Gesammelte Abhandlungen - Collected Papers I: 1951-1962 (Springer Collected Works in Mathematics)

Friedrich Hirzebruch (1927 –2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure of his generation. Hirzebruch’s first great mathematical achievement was the proof, in 1954, of the generalization of the classical Riemann-Roch theorem to higher dimensional complex manifolds, now known as the Hirzebruch-Riemann-Roch theorem. This used the new techniques of sheaf cohomology and was one of the centerpieces of the explosion of new results in geometry and topology during the 1950s. Further generalization of this led to the Grothendieck-Riemann-Roch theorem, and the Atiyah-Singer index theorem. He received many awards and honors, including the Wolf prize in 1988, the Lobachevsky prize in 1990, and fifteen honorary doctorates. These two volumes collect the majority of his research papers, which cover a variety of topics. In zwei Bänden sind fast alle Veröffentlichungen enthalten, die F. Hirzebruch verfasst hat.

Gesammelte Abhandlungen - Collected Papers II: 1963 - 1987 (Springer Collected Works in Mathematics)

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