By Maria Emilia Alonso, Enrique Arrondo, Raquel Mallavibarrena, Ignacio Sols
This quantity is a homage to the reminiscence of the Spanish mathematician Federico Gaeta (1923-2007). except a historic presentation of his lifestyles and interplay with the classical Italian institution of algebraic geometry, the amount offers surveys and unique learn papers at the arithmetic he studied. particularly, it's divided into 3 elements: linkage conception, Schottky challenge and invariant conception. in this final subject a hitherto unpublished article via Federico Gaeta can also be integrated.
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Additional resources for Liaison, Schottky Problem and Invariant Theory: Remembering Federico Gaeta
We are led to pose the following question: Question 17. Let Vn−c ⊂ Pn be a matrix variety of codimension c. Can Vn−c be obtained by a chain of complete simple intersections, starting from a complete simple intersection of n − c forms? The answer to the above question as well as to Question 9 is no, in general. In other words, in the classical context of Liaison Theory, Gaeta’s Theorem does not generalize to varieties of higher codimension. See  or – for more information. Going on with the problem of classifying space curves, in  and , F.
To characterize licci curves in P3 ). F. Gaeta solved this problem in a masterly and elegant way; this was a seminal work in Liaison Theory and his most important contribution to this active area of research. Historically Liaison began in the nineteenth century as a tool to study and classify curves in projective spaces and it goes back at least to work of M. Noether, F. S. Macaulay. The initial idea was to start with a curve in P3 and to study its residual in a complete intersection. It turns out that a lot of information can be carried over from a Partially supported by MTM2007-61104.
Franchetta tells me that once Gaeta reported to him about harsh contrasts, for political reasons, with the faculty. Once more I can refer to , who, commenting in a footnote upon the heavy atmosphere which at that time reigned at the faculty of Sciences of Zaragoza, says: Hasta en la orla de ﬁn de carrera de mi promoci´ on se aprecia el desastre. Figuran en la ella los Prof. Garc´ıa Atance, Arajuo, I˜ niguez, Rodr´ıguesSalinas, Cabrera, Servera, Liso, Rodr´ıgues Vidal, Burbano y Gaeta, pero este u ´ltimo nos pidi´ o estar lejos de sus colegas, entre los alumnos .