Dionisio Gallarati (May 8, 1923 – May 13, 2019) was an Italian mathematician, who specialised in

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

. He was a major influence on the development of algebra and geometry at the

University of Genova The University of Genoa () is a Public university, public research university. It is one of the largest universities in Italy and it is located in the city of Genoa, on the Italian Riviera in the Liguria region of northwestern Italy. The original ...

Life

Born 8 May 1923 in

Savona Savona (; ) is a seaport and (municipality) in the west part of the northern Italian region of Liguria, and the capital of the Province of Savona. Facing the Ligurian Sea, Savona is the main center of the Riviera di Ponente (the western se ...

, Italy, Gallarati joined the

University of Pisa The University of Pisa (, UniPi) is a public university, public research university in Pisa, Italy. Founded in 1343, it is one of the oldest universities in Europe. Together with Scuola Normale Superiore di Pisa and Sant'Anna School of Advanced S ...

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 Giacomo Albanese (11 July 1890 – 8 June 1947) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in the University of São Paulo, Brazil, in 1936. Biography Albanese attended the school in Palerm ...

, Leonard Roth,

Leonida Tonelli Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian people, Italian mathematician, noted for proving Fubini's theorem#Tonelli's theorem for non-negative measurable functions, Tonelli's theorem, a variation of Fubini's theorem, and f ...

, 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 in 1936, at the first delivery. Severi was born in Arezzo, Italy. He is famous for his contributions to algebra ...

. 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 exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concep ...

complexes containing the curve in the

Grassmannian In mathematics, the Grassmannian \mathbf_k(V) (named in honour of Hermann Grassmann) is a differentiable manifold that parameterizes the set of all k-dimension (vector space), dimensional linear subspaces of an n-dimensional vector space V over a ...

corresponding to the tangent lines of a nondegenerate

projective curve In algebraic geometry, a projective variety is an algebraic variety that is a closed subvariety of a projective space. That is, it is the zero-locus in \mathbb^n of some finite family of homogeneous polynomials that generate a prime ideal, the de ...

." 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 papyru ...

Works

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

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...

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