Gesammelte Abhandlungen - Collected Papers II 1963 - 1987

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.

34. The topology of normal singularities of an algebraic surface (d’après un article de D. Mumford).- 36. Bericht über Arbeiten am Mathematischen Institut der Universität Bonn.- 37. Elliptische Differentialoperatoren auf Mannigfaltigkeiten.- 38. Über Singularitäten komplexer Flächen.- 39. Singularities and exotic spheres.- 40. Involutionen auf Mannigfaltigkeiten.- 41. (mit K. Jänich) Involutions and Singularities.- 42. The signature of ramified coverings.- 43.(mit M.F. Atiyah) Spin-manifolds and group actions.- 44. Lösung einer Aufgabe von H. Hasse.- 45. Free involutions on manifolds and some elementary number theory.- 46. Pontrjagin classes of rational homology manifolds and the signature of some affine hypersurfaces.- 47. The signature theorem: Reminiscences and recreation.- 48. The Hilbert modular group, resolution of the singularities at the cusps and related problems.- 49. (mit H. Behnke) In memoriam Heinz Hopf.- 50. The Hilbert modular group and some algebraic surfaces.- 51. Hilbert modular surfaces.- 52. (mit W. F. Hammond) L-series, modular imbeddings and signatures.- 53. (mit A. Van de Ven) Hilbert modular surfaces and the classification of algebraic surfaces.- 55. Kurven auf den Hilbertschen Modulflachen und Klassenzahl-relationen.- 56. Hilbert modular surfaces and class numbers.- 57. Hilberts’s modular group of the field $$\mathbb (\sqrt{5})$$ and the cubic diagonal surface of Clebsch and Klein.- 60. (mit D. Zagier) Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus.- 61. (mit D. Zagier) Classification of Hilbert modular surfaces.- 62. The ring of Hilbert modular forms for real quadratic fields of small discriminant.- 63. Modulflächen und Modulkurven zur symmetrischen Hilbertschen Modulgruppe.- 64. Überlagerungen der projektiven Ebene und Hilbertsche Modulflachen.- 65. (mit A. Van de Ven) Minimal Hilbert modular surfaces with pg = 3 and K2 = 2.- 66. The canonical map for certain Hilbertmodular sufaces.- 67. The icosahedron.- 68. Some examples of algebraic surfaces.- 69. Arrangements of lines and algebraic surfaces.- 70. Mannigfaltigkeiten und algebraische Topologie.- 71. Chern numbers of algebraic surfaces — an example.- 73. Algebraic surfaces with extreme Chern numbers.- 74. Singularities of algebraic surfaces and characteristic numbers.- 75. Some examples of threefolds with trivial canonical bundle.- Kommentare.- Schriftenverzeichnis.- Danksagung.