People always refer to the Italians as great algebraic geometers. ``The Italian School of algebraic geometry" it is referred to. I decided to do a little research with Professors and my library on the names and the kind of results that they got back at the begin of the 20th century.
Names that get into this are: Cremona, Severi, Eniques, Segre, Castelnuovo, Fano, Veronese, Bertini.
Partly the reason I got interested in this (not to mention I like algebraic geometry) is the following.
In 1900 David Hilbert proposed a list of guiding problems in mathematics. The 15th of such problems roughly speaking calls for rigorous foundations for intersection theory in algebraic geometry. Back then, Severi (who was a major figure in the community) supported Schubert's point of view on the subject. That is, trying to make rigorous Schubert's work. One of the tools Schubert used was for example the so-called ``Principle of conservation of number" (PCN) which turned out to be wrong (as we will show by example next time).
Coming up next week, the sequel of this post will be about examples for which the PCN goes wrong.
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