Italian School Of Algebraic Geometry Research Articles

Italian and Polish Mathematicians Face Racial Persecution and Emigration: Backgrounds, Individual Fates and Global Aspects

This paper provides a new analytical perspective on the socio-cultural interactions involving members of two main Italian research communities – the School of Mathematical Logic and the Italian School of Algebraic Geometry – and some of their Polish colleagues (Samuel Dickstein, Wiesław Jezierski, Alfred Rosenblatt et al.). I shall argue that the intricate network of relationships between Giuseppe Peano, Corrado Segre and their protégés paved the way for an intensification of scientific exchanges between Italy and Poland in the 1930s. The climax manifested in visits by Tullio Levi-Civita and Mauro Picone to Warsaw and Krakow. Simultaneously, this network fostered instances of remarkable cross-solidarity when Polish and Italian mathematicians faced a period of severe anti-Semitic persecution and migration. An appendix containing unpublished letters documents Rosenblatt’s role in assisting aspiring Italian refugees in securing positions in Peru.

Tra le carte di Gino Fano: le ricerche sulle varietà a tre dimensioni

AbstractThis paper investigates G. Fano’s contributions to the study of three-dimensional varieties—the so called Fano threefolds—starting from unpublished manuscripts kept in Turin’s Special Mathematical Library. The main aspects examined are the evolution of the research path, the placing into the wake of the Italian school of algebraic geometry, Fano’s links with the English geometers and his legacy on later studies.

Objectivity and Rigor in Classical Italian Algebraic Geometry

The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon –Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely objectivity as faithfulness to facts and objectivity as intersubjectivity.

From Plato to Weil and beyond: Genericity through the history of mathematics

At the end of the 19th century, genericity took an important step toward mathematical analysis, due to the developments promoted by the Italian school of algebraic geometry. However, its origins can be traced back to ancient mathematics in the work of prominent philosophers and mathematicians, such as Plato and Euclid. In this article, we will try to show how a key notion in the structuralist turn of algebraic geometry evolved from a vague linguistic phenomenon and became a precise and fruitful mathematical concept.

Obituary: Anna Morpurgo Davies

Historical linguists are sometimes thought to spend their time deciphering unknown scripts and languages, although in reality most of them just look at the history of perfectly well-understood tongues. Anna Morpurgo Davies, a world-leading figure in the study of Ancient Greek and Anatolian, who has died aged seventy-seven, was among the select few to do both. Born in Milan, Italy, daughter of Maria (nee Castelnuovo) and Augusto Morpurgo, she moved to Rome upon the death of her father in 1939. For a (secular) Jewish family those were difficult years, and Anna survived the war only with luck and in hiding. Attending the Liceo Classico Giulio Cesare in Rome, and inspired by her grandfather, Guido Castelnuovo, a leader of the Italian school of algebraic geometry, she initially felt drawn towards mathematics, but then decided to study classics at the University of Rome, out of interest in classical literature and the history of religion. In a compulsory course on historical grammar, one of her teachers, Carlo Gallavotti, introduced her to Linear B, a syllabic script used to write Greek during the later second millennium bc, which had only just been deciphered. Fascinated by the prospect of participating in the discovery of an entirely new period of Ancient Greek language and culture, she turned towards historical linguistics as the necessary key to it. After graduating in 1959, she became Gallavotti’s assistant and began to work on the first lexicon of Mycenaean, the early dialect in which the Linear B texts were written; this was published in 1963 and remained a standard work for several decades. In 1961 she obtained a junior fellowship at the newly founded Centre for Hellenic Studies in Washington. Until this point, Anna had been largely self-trained in linguistic theory; in the US, she had her first real experience of the world of theoretical linguistics. Although her own work was to remain focused on the historical and comparative study of languages, she acquired a profound interest in general linguistics, too, so much so that she later became a driving force behind the establishment of a chair in linguistics at Oxford. Still in Washington, she met the historian John K. Davies, whom she married a year later and with whom she moved to Oxford in 1962; the marriage was dissolved in 1978, but Oxford remained the centre of her personal and academic life.

Corrado Segre. A life dedicated to training young researchers

Segre was one of the most important architects of the “Risorgimento of geometry in Italy”. Under his guidance, in the period from 1891 to 1912, the Italian School of algebraic geometry was consolidated and, in just few years, Italy would assume a leading position on the international scene. Segre’s university courses were a real breeding ground for future researchers. Numerous young mathematicians prepared their degree theses with him on the most advanced sectors of geometry, including G. Fano, B. Levi, F. Severi, A. Terracini, and E. Togliatti. A number of newly graduated students from Italy and abroad, attracted by Segre’s fame, came to Turin to hear his lectures. Among them there were high-profile mathematicians from Italy, including G. Castelnuovo, F. Enriques, G. Scorza, as well as from abroad, such as W. H. Young and G. Chisholm, J. Coolidge and C. H. Sisam. In this paper this period of flourishing of the Italian School of algebraic geometry is illustrated and the significant role of Segre’s lessons in stimulating and fostering the research of his disciples is highlighted, as well as his idea of School.

The birth of a School

At the end of the 1880s, Corrado Segre directed Guido Castelnuovo to the study of geometry on algebraic curves: this heralded the birth of the Italian School of algebraic geometry, and Castelnuovo was to be come the first of Segre’s many disciples, direct or indirect. Just a short time later, Federigo Enriques came into contact with Segre, attracted by the young master’s reputation and by the liveliness of the Torino milieu. He was instead destined for Rome, where his study of surfaces was supervised by Castelnuovo. Segre followed his results at a distance, while in the meantime attempting to derive a rigorous proof of the resolution theorem of singularities. The acquaintances of Segre, Castelnuovo and Enriques transformed into a scientific fellowship and they even planned to collaborate on the writing of a general treatise, but this was never realised.

The Luigi Cremona Archive of the Mazzini Institute of Genoa

Luigi Cremona (1830–1903) is unanimously considered to be the man who laid the foundations of the prestigious Italian school of Algebraic Geometry. In this paper we draw attention to the “Legato Itala Cremona Cozzolino”, which was given to the library of the Mazzini Institute, Genoa, Italy, by Cremona’s daughter, Itala, probably in 1939. This legacy, which contains over 6000 documents, mainly consisting of Cremona’s correspondence with scientific and institutional Italian interlocutors, can help us to understand the connections between the development of Italian mathematics in the second half of the XIX century and the main political issues of Italian history.

Notes on the correspondence between Luigi Cremona and Max Noether

This paper contains an analysis of the scientific climate in which the Italian school of algebraic geometry came into being and developed in a direction different from that of the German school, even though both shared a common initial matrix. Reference is made to a number of letters written by Max Noether to Luigi Cremona.