Antonius Van de Ven

Antonius Josephus Hubertus Marie "Ton" Van de Ven (born May 11, 1931 in Cadier en Keer , Province of Limburg , † December 10, 2014 in Leiderdorp ) was a Dutch mathematician who dealt with algebraic geometry .

Antonius Van de Ven (right) 1977 with Otto Haupt in Erlangen

Antonius Van de Ven went to school in Maastricht and from 1948 studied mathematics at the University of Leiden , where he completed his doctoral examination in 1954 and received his doctorate in 1957 under Willem Titus van Est (Over de homologiestructuur van enige typen vezelruimten). Other of his teachers were Hendrik Kloosterman , Johannes Drost , Tonny Albert Springer and Johannes Haantjes . At times he also tended to the basics of mathematics and studied with Arend Heyting and Evert Willem Beth in Amsterdam. In 1954 he was in Rome, where he worked with the algebraic geometers Edoardo Vesentini , Beniamino Segre and Francesco Severi and then at the ETH Zurich with Heinz Hopf , Beno Eckmann and Armand Borel , among others , whereby the contact with Borel was of particular importance for his dissertation . After his dissertation he was a research assistant at the University of Leiden and from 1959 to 1961 at the recommendation of Armand Borel at the Institute for Advanced Study at Kunihiko Kodaira . From 1961 he was lecturer and from 1963 professor at the University of Leiden. In 1996 he retired.

His dissertation was on the topological structure (characteristic classes) of vector space bundles over algebraic varieties. In 1966 he proved that for compact complex surfaces of general type for the Chern classes the inequality fulfilled (later van de Ven assumed that it could be improved to, which Yōichi Miyaoka and Shing-Tung Yau proved independently in 1978 , it is also called Bogomolov-Miyaoka- Called Yau inequality). He showed, among other things, that the almost complex manifolds introduced by Heinz Hopf and Charles Ehresmann do not always allow a complex structure (he gave four-dimensional counterexamples). ${\displaystyle c_{1}^{2}\leq 8c_{2}}$ ${\displaystyle c_{1}^{2}\leq 3c_{2}}$

He worked with Friedrich Hirzebruch and Gerard van der Geer on Hilbert's modular surfaces and their classification in the classification of complex surfaces. With Egbert Brieskorn he published about exotic complex structures on products of homotopy spheres. He was friends with Hirzebruch and Brieskorn. Together with Wolf Barth , he examined vector bundles in projective spaces and for Grassman manifolds. Both proved that a holomorphic 2-bundle splits on a projective space if the dimension of the space is big enough. In 1979 he answered a question from Hans Grauert by giving an example of a space curve whose normal bundle cannot be embedded. With Christian Okonek , he dealt with topological and differentiable structures of complex surfaces and 3 varieties. In 1985 he gave an example of a complex surface that is not isomorphic to an eight times inflated projective plane, but is homeomorphic to it. In 1989 he showed with Okonek that they also have different differentiable structures. After Simon Donaldson with had given an example of a 4-manifold with two differentiable structures showed Okonek and van de Ven (and independent John Morgan and Robert Friedman ) that there are infinitely many differentiable structures in this area are. They were naturally given by familiar algebraic surfaces. Since these are classified by their Kodaira dimension and the differentiability structure also varied with the Kodaira dimension in all cases, van de Ven assumed that this is a differential topological invariant (proven by Robert Friedman and Z. Qin 1994). ${\displaystyle \mathbb {P} ^{2}\#9\cdot {\bar {\mathbb {P} }}^{2}}$

His book on compact complex surfaces, first published in 1984 with Wolf Barth and Chris Peters, is a standard work.

In 1985 he became a member of the Royal Netherlands Academy of Sciences. In 1965 he received the Shell Prize for Mathematics and in 1966 he became a member of the Koninklijke Hollandsche Maatschappij der Wetenschappen. He was visiting professor at the Tata Institute for Fundamental Research and at the ETH Zurich. He refused calls to Heidelberg, Göttingen, Münster and Munich and stayed in Leiden.

Chris Peters and Gerard van der Geer are among his PhD students .

Fonts

• with Chris Peters, Klaus Hulek , Wolf Barth Compact complex surfaces (= results of mathematics and its border areas. ) Springer, 1984, 2nd edition 2004.
• with Robert Lazarsfeld : Topics in the geometry of projective space. Recent work of FL Zak. Birkhäuser 1984.

Individual evidence

1. ^ Levens report Ton van de Ven
2. ^ Mathematics Genealogy Project
3. ↑ Okonek, van de Ven, Stable bundles and differentiable structures on certain elliptic surfaces, Invent. Math., Volume 86, 1986, pp. 357-370, SUB Goettingen
4. ↑ Van de Ven, On the differentiable structure of certain algebraic surfaces, Seminaire Bourbaki 667, 1986, Astérisque 145/146 1987