Guido Castelnuovo

Guido Castelnuovo (14 August 1865, Venice – 27 April

Work

In Turin Castelnuovo was strongly influenced by Corrado Segre. In this period he published high-quality work on algebraic curves. He also made a major step in reinterpreting the work on linear series by Alexander von Brill and Max Noether (Brill-Noether theory).

Related Topics:
Turin - Corrado Segre - Algebra - Curve - Linear series - Alexander von Brill - Max Noether - Brill-Noether theory

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Castelnuovo had his own theory about how Mathematics should be taught. His courses were divided into two: first a general overview of mathematics, and then a in-depth theory of algebraic curves. He has said about this approach:

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:? the reason for the division is that on the one hand it is necessary to have general culture, on the other hand it is necessary to have deep knowledge of a particular field.

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He also taught courses on algebraic functions and abelian integrals. Here, he treated, among other things, Riemann surfaces, non-Euclidean geometry, differential geometry, interpolation and approximation, and probability theory. He found the latter the most interesting, because as a relatively recent one, the relationship between the deduction and the empirical contribution was more clear. In 1919, he published Calcolo della probabilità about this subject. He also wrote a book on calculus: Le origini del calcolo infinitesimale nell'era moderna.

Related Topics:
Algebraic function - Abelian integral - Riemann surfaces - Non-Euclidean geometry - Differential geometry - Interpolation - Approximation - Probability theory - 1919 - Calculus

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Castelnuovo's most important work was done in the field of algebraic geometry. In the early 1890s he published three famous papers, including one with the first use of the characteristic linear series of a family of curves. The Castelnuovo-Severi inequality was co-named after him. He collaborated with Federigo Enriques on the theory of surfaces. This collaboration started in 1892 when Enriques was only a student, but grew further over the next 20 years: they submitted their work to the Royal Prize in Mathematics by the Accademia dei Lincei in 1902, but were not given the prize because they had sent it jointly instead of under one name. Both received the prize in later years.

Related Topics:
Algebraic geometry - 1890s - Characteristic linear series of a family of curves - Castelnuovo-Severi inequality - Federigo Enriques - 1892 - Royal Prize in Mathematics - Accademia dei Lincei - 1902

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Another theorem named partly after Castelnuovo is the Kronecker-Castelnuovo theorem (1894): If the sections of an irreducible algebraic surface, having at most isolated singular points, with a general tangent plane turn out to be reducible curves, then surface is either ruled surface and in fact a scroll, or the Veronese surface. Kronecker never published it but stated it in a lecture. Castelnuovo proved it. In total, Castelnuovo published over 100 articles, books and memoirs.

Related Topics:
Kronecker-Castelnuovo theorem - Algebraic surface - Singular point - Reducible - Ruled surface - Veronese surface

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