482 research outputs found
Remarks on the relations between the Italian and American schools of algebraic in the first decades of the 20th century
No full textIn this paper we give an overview of the interactions between Italian and American algebraic geometers during the first decades of the 20th century. We focus on three mathematicians—Julian L. Coolidge, Solomon Lefschetz, and Oscar Zariski—whose relations with the Italian school were quite intense. More generally, we discuss the importance of this influence in the development of algebraic geometry in the first half of the 20th centur
Seminario Nazionale sui Licei Matematici
No full textgiovedì 21 settembre pomeriggio
15.00 Apertura dei lavori
15.15 Ileana Rabuffo (Università di Salerno – Presidente della Commissione Didattica
Permanente della Società Italiana di Fisica), L’eleganza della matematica: una risorsa per la
fisica
16.00 Paolo Maroscia (Sapienza Università di Roma, gruppo “Matematica e Letteratura”),
Perché collegare la matematica e la letteratura, e come? Riflessioni e proposte
16.45 break
17.00 LABORATORI
venerdì 22 settembre mattina
9.00 Saluti istituzionali al Convegno
9.30 Francesco Saverio Tortoriello: La nascita e lo sviluppo del Liceo Matematico
10.00 PANEL SUI MODELLI FORMATIVI DELLE SEDI CHE HANNO ATTUATO IL LM (struttura e organizzazione generale: quadri orari, ruolo degli insegnanti e degli universitari, modelli per la formazione degli studenti e degli insegnanti, convenzioni, legami con il PLS, prova d’ingresso, valutazione, ...) – intervengono: Claudio Bernardi (La Sapienza Università di Torino), Antonio di Nola (Università di Salerno), Ornella Robutti (Università di Torino)
11.00 DISCUSSIONE
11.30 break
12.00 INTERVENTO/I di rappresentanti MIUR o USR
venerdì 22 settembre pomeriggio
15.00 PANEL SULLE ESPERIENZE FORMATIVE DELLE SEDI CHE HANNO ATTUATO IL LM (finalità, obiettivi, contenuti matematici e contenuti interdisciplinari, attività, programmazione) – intervengono: Ferdinando Arzarello (Università di Torino), Roberto Capone (Università di Salerno), Enrico Rogora (Sapienza Università di Roma)
16.00 DISCUSSIONE
16.30 INTERVENTI
17.30 break
18.00 INTERVENTI
19.00 DISCUSSIONE
sabato 23 settembre mattina
9.00 INTERVENTI
10.00 DISCUSSIONE
10.30 break
11.00 TAVOLA ROTONDA ISTITUZIONALE E CULTURALE sul tema Il liceo matematico: un’occasione per ripensare l’insegnamento della matematica nelle Superiori – relatori: Ciro Ciliberto, Roberto Tortora, Daniele Boffi
12.00 DISCUSSIONE SULLA TAVOLA ROTONDA
12.30 PROPOSTE PER IL FUTURO
13.00 CONCLUSIONE DEI LAVOR
Birational geometry of surfaces. Preface
No full textThis volume is an issue of the Bollettino dell’Unione Matematica Italiana connected to the workshop “Birational geometry of surfaces” which took place at the Department of Mathematics of the University of Rome “Tor Vergata”, Italy, in January, 11–15, 2016. We thank the Editors of the Bollettino dell’Unione Matematica Italiana for having accepted to dedicate this issue to this topic.
The workshop was organized by Ciro Ciliberto, Thomas Dedieu, Flaminio Flamini, Rita Pardini with the support of the projects:
Geometria, Algebra e Combinatoria di Spazi di Moduli e Configurazioni—no. PRA-2016-67—of the University of Pisa,
National Research Project (PRIN 2010-11) Geometria delle Varietà Algebriche—no. 2010S47ARA-005—(nodes of Pisa and Roma “Tor Vergata”),
GDRE (CNRS-INdAM) GRIFGA 2012–2015,
Families of subvarieties in complex algebraic varieties; this project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 652782
On Cremona contractibility
No full textWe give a constructive proof of a classical theorem which determines irreducible plane curves that are contractible to a point by a Cremona transformation. The problem of characterizing Cremona contractible (not necessarily irreducible) hypersurfaces in a projective space is in general widely open: we report on the only known result about reducible plane curves consisting of two components, due to litaka, and we discuss a couple of examples concerning plane curves with more components. Finally, we prove that all varieties of codimension at least two in a projective space are Cremona contractible to a point
The Italian school of algebraic geometry and Abel's legacy
No full textTHE ITALIAN SCHOOL OF ALGEBRAIC GEOMETRY AND
ABEL’S LEGACY
ALDO BRIGAGLIA, CIRO CILIBERTO, AND CLAUDIO PEDRINI
Introduction
Exactly one century ago, in the spring of 1902, the prestigious mathematical journal Acta Mathematica, decided to mark the centenary of Abel’s birth by dedicating three issues to the memory of this Norwegian mathematician. Some of the most influential Italian mathematician of the day were invited to contribute to these issues. Among those invited were Guido Catelnuovo, at the time the most well-known representative of the Italian school of algebraic geometry, and Federigo Enriques. Enriques, at first, accepted the invitation and, as he communicated to Castelnuovo, decided to write ... una specie di Bericht, breve, intorno ai nostri lavori, in cui mi propongo di esporre la teoria sotto l’aspetto analitico.
( ... a kind of Bericht, a short one, concerning our papers, in which I would like to expose the theory using the analytic viewpoint.)
(letter of 13/3/1902, for all citations from the correspondence between Enriques and Castelnuovo, see [BCG]).
The project was never completed. However this short citation is important for us: it tells us, in fact, that the Italian algebraic geometers, at the beginning of last century, used to look at their connections with Abel via analytic and transcendantal methods. Although never really central in the Italian school were, this attitude
was always considered as a natural counterpart of the projective-geometric aspects typical of the Italians. Furthermore, as we will see, at the time Enriques was writing, there was in Italy an important revival of analytic ideas.
In this paper we will try to make clear an interesting set of contributions which,
inside the Italian school, were, in Enriques’ sense, inspired by Abel’s analytic viewpoint.
For this we will go back to the real beginning of the italian school with Luigi Cremona, who is considered to be its founder. Then we will follow the evolution of these ideas up until the 1930’s and we will indicate how they are thought of today.
Abel, apparently, never had any contact with the Italian mathematical environment,in his short life, nor even specifically during his travels to Italy (see [St]).
Therefore, his influence on Italian mathematicians was late and indirect. However,
we believe that, despite this, it has been deep and longstanding.
In the first chapter we will give an overview of the influence of Abel’s ideas on the beginnings of the Italian school, filtered via Riemann’s viewpoint and the geometric interpretation of it by Clebsch and Gordan, and later by Brill and Noether. This chapter mainly centers around the character of Luigi Cremona, the founder of the
Italian school.
In the second chapter we will see how Abel’s influence was still active at the beginning of the XXth century and played a basic role in understanding the notion of irregularity of surfaces. The main characters, in this period, are the young Severi and the well established Caselnuovo, whose contributions we will review, indicating also their subsequent far reaching influence inside and outside the Italian school,
until A. Weil’s proof of Riemann’s hypotheses for the zeta function of an algebraic curve over a finite field.
The third chapter is devoted to Severi’s ideas on rational equivalence of 0-cycles on a surface. We will indicate how some of these ideas were related, in Severi’s mind, to Abel’s viewpoint. As is well known, Severi’s contributions on the subject have been very controversial. We will briefly report on the main criticisms but we will also try to elucidate which of them have a present validity. In particular we will direct our, and we hope the reader’s attention, to some of his ideas which are very closely related to Bloch’s conjecture. We dedicate a few, more technical, sections at the end of chapter 3 to open a window on the present developments of this last
subject, specifically to some motivic interpretations which we think are rather close
to Severi’s original viewpoint.
Due to the different tastes and attitudes of the authors, which we deliberately did not make too much effort to hide, the paper is rather uneven. The first chapter is expository and more historiographical in nature. The other two, though sharing with the first a historiographical perspective, have a different flavour: in the second some technical aspects start to appear, and they become even more relevant in chapter 3, especially, as we said, in its last sections. We hope that the uneveness
of the paper will attract, rather than repel, readers with different interests
On the Cremona contractibility of unions of lines in the plane
No full textWe discuss the concept of Cremona contractible plane curves, with a historical account on the development of this subject. Then we classify Cremona contractible unions of d ≥ 12 lines in the plane
The general ternary form can be recovered by its Hessian
No full textThe Hessian map is the rational map that sends a homogeneous polynomial to
the determinant of its Hessian matrix. We prove that the Hessian map is
birational on its image for ternary forms of degree , , by
considering the action of the orthogonal group. In a previous paper we proved
the analogous result for binary forms, with more geometric techniques.Comment: by Ciro Ciliberto, Giorgio Ottaviani, with an appendix by Jerson
Caro, Juanita Duque-Roser
Corrigendum to: Classification of varieties with canonical curve section via Gaussian maps on canonical curves
No full text- …
