Dionisio Gallarati (May 8, 1923 – May 13, 2019) was an Italian mathematician, who specialised in algebraic geometry. He was a major influence on the development of algebra and geometry at the

University of Genova The University of Genoa, known also with the acronym UniGe ( it, Università di Genova), is one of the largest universities in Italy. It is located in the city of Genoa and regional Metropolitan City of Genoa, on the Italian Riviera in the Liguri ...

Life

Born 8 May 1923 in Savona, Italy, Gallarati joined the

University of Pisa The University of Pisa ( it, Università di Pisa, UniPi), officially founded in 1343, is one of the oldest universities in Europe. History The Origins The University of Pisa was officially founded in 1343, although various scholars place ...

in 1941. His studies being interrupted by the war, he received his first degree from Genova.www-history.mcs.st-andrews.ac.uk/Biographies/Gallarati.html He started his research career at l'Istituto Nazionale di Alta Matematica in Rome, where he was taught by Giacomo Albanese, Leonard Roth,

Leonida Tonelli Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian mathematician, noted for creating Tonelli's theorem, a variation of Fubini's theorem, and for introducing semicontinuity methods as a common tool for the direct method in the calc ...

, E. G. Togliatti,

Beniamino Segre Beniamino Segre (16 February 1903 – 2 October 1977) was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of finite geometry. Life and career He was born and studied in Turin ...

and

Francesco Severi Francesco Severi (13 April 1879 – 8 December 1961) was an Italian mathematician. He was the chair of the committee on Fields Medal on 1936, at the first delivery. Severi was born in Arezzo, Italy. He is famous for his contributions to algeb ...

. He took a post at Genova in 1947, where he stayed until he retired in 1987.

Research

Gallarati published 64 papers between 1951 and 1996. Important amongst his research was the study of surfaces in P³ with multiple isolated singularities. His lower bounds for maximal number of nodes of surfaces of degree ''n'' stood for a long time, and exact solutions for large ''n'' were still unknown in 2001. In Grassmannian geometry he extended Segre's bound "for the number of

linearly independent In the theory of vector spaces, a set of vectors is said to be if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be . These concepts are ...

complexes containing the curve in the

Grassmannian In mathematics, the Grassmannian is a space that parameterizes all -dimensional linear subspaces of the -dimensional vector space . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the projective ...

corresponding to the tangent lines of a nondegenerate

projective curve In algebraic geometry, a projective variety over an algebraically closed field ''k'' is a subset of some projective ''n''-space \mathbb^n over ''k'' that is the zero-locus of some finite family of homogeneous polynomials of ''n'' + 1 variables ...

." He extended the results to arbitrarily dimensioned

varieties Variety may refer to: Arts and entertainment Entertainment formats * Variety (radio) * Variety show, in theater and television Films * ''Variety'' (1925 film), a German silent film directed by Ewald Andre Dupont * ''Variety'' (1935 film), ...

' tangent spaces, to higher degree complexes, and to arbitrary curves in Grassmannians corresponding to degenerate

scrolls A scroll (from the Old French ''escroe'' or ''escroue''), also known as a roll, is a roll of papyrus, parchment, or paper containing writing. Structure A scroll is usually partitioned into pages, which are sometimes separate sheets of papy ...

Works

Gallarati wrote three books and 64 papers, in algebraic geometry, differential geometry,

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined o ...

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

, and biography. His co-authors include Giulio Aruffo, Mauro C. Beltrametti, Maria Teresa Bonardi, Gabriella Canonero, Ettore Carletti, Enrica Casazza, Mario G. Galli, Aldo Monti Iandelli, Giacomo Bragadin, Giorgio Luigi Olcese, Giulio Passatore, Luigi Robert, Aldo Rollero, Michele Sarà, Giulio Scarsi and Maria Ezia Serpico. 33 of his papers are collected in ''Dionisio Gallarati: Collected Papers of Dionisio Gallarati'' Kinston, Ontario, 2000, ed A. V. Geramita.

References

{{DEFAULTSORT:Gallarati, Dionisio 1923 births Italian mathematicians 2019 deaths University of Pisa alumni University of Genoa alumni