Program Overview

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University Program Information

The Scuola Normale Superiore (SNS) offers various academic programs and research opportunities.

Faculties

• Faculty of Humanities
• Faculty of Sciences
• Faculty of Political and Social Sciences

Teaching Syllabus

The SNS provides a comprehensive teaching syllabus, including:

• Faculty of Humanities
• Faculty of Sciences
• Faculty of Political and Social Sciences
• Study regulations
• Seminars
• Foreign Languages
  • English Courses and Materials
• Course archive
• Admission to single courses

College Life

The university offers a range of college life activities, including:

• Colleges and canteen
• Places
• Library
• Collaboration opportunities
• Peer tutoring
• Financing opportunities
• Psychological wellbeing and support
• Disability support
• Student activities

Why Apply to the Normale?

The SNS offers several reasons to apply, including:

• At the forefront of tradition
• A hotbed of talents
• The quality of training and research
• Connected to the world
• Study free of charge
• An ideal setting

Placement

The university provides placement opportunities, including:

• Incoming internships
• Outgoing Internships
• Customised orientation and consultancy
• Placement seminars
• Placement portals
• JOBFair
• For companies and institutions
• Alumni and Mentoring

Admissions

The SNS offers various admission options, including:

• Undergraduate
• PhD
• National Doctorates and Joint PhD at Partner Universities

Research and Innovation

The university is committed to research and innovation, with:

• Cutting-edge research
• Departments of Excellence
• Knowledge transfer
• Open Science
• Dissemination of research
• Research Quality Assessment (VQR)

Research Structures

The SNS has various research structures, including:

• Laboratories and Centres
• Research groups
• Support Centres

Tools for Research

The university provides tools for research, including:

• Research opportunities and funding
• Training activities and information
• Knowledge and technology transfer
• The Joint Ethical Committee for Research

Public Engagement

The SNS is committed to public engagement, with:

• The "Normale delle Idee"
• The "Concerti della Normale"
• Il Cinema della Normale
• Communicating research
• The students' forum
• The "Letture della Normale"
• Contemporary art at the Carovana
• Piazza dei Cavalieri Project
• Third mission/Public Engagement co-ordination

Dissemination of Research

The university disseminates research through:

• Meetings, conferences and workshops
• The Colloqui della Classe di Scienze

Valorisation of Research

The SNS valorises research through:

• Placement
• Trasferimento della conoscenza
• Open Science
• Gestione dei dati della ricerca
• Open access alle pubblicazioni

Course Details: Algebraic Surfaces

Period of Duration of Course

The course runs from October 2025 to May 2026.

Course Info

• Number of course hours: 40
• Number of hours of lecturers of reference: 40
• CFU: 6

Modalitŕ Esame

The exam is an oral exam.

Lecturer

The lecturer is Angelo Vistoli.

Prerequisiti

The prerequisites for the course are the content of the courses "Scheme Theory I" and "Scheme Theory II", and it is available for Master's and PhD programs.

Programma

The course covers the following topics:

• Smooth projective surfaces
• Divisors, intersection numbers
• Hodge index theorem
• Riemann-Roch
• Blow-ups, rational maps
• Ruled surfaces
• Canonical maps
• Kodaira dimension
• Enriques classification

Obiettivi Formativi

The course aims to teach the theory of algebraic surfaces.

Riferimenti Bibliografici

The recommended textbooks are:

• Robin Hartshorne, Algebraic Geometry, Springer Verlag
• Lucian Bdescu, Algebraic Surfaces, Springer Verlag
• Arnaud Beauville, Complex Algebraic Surfaces, Cambridge University Press