Università di Roma “Tor Vergata”

Corso di Laurea Magistrale in Matematica

Pagina soggetta ad aggiornamenti frequenti

Algebraic Geometry

II Semester 02/03/2015 - 05/06/2015 – 8 credits (64 hours)

Lecturer Prof. Flaminio Flamini (flamini[ANTISPAM]@mat.uniroma2.it)

Lectures (course in English on demand)
Tuesday & Wednesday (Mart-Merc)/ 11:00-13:00 / Room 1101 (D'Antoni).

Friday (Ven)/ 9:00-11:00 / Room 1101 (D'Antoni).

Office hours Friday, 11:00-13:00, Office 1116 (Piano 1, Dente 1)

· Tentative program

· Daily calendar of lectures



Lecture Notes: preliminary drafts


· NOTE CORSO di F. Flamini
Versione completa per studenti, contiene tutto cio' di cui si e' parlato nel corso (NON DISTRIBUIRE). Probabilmente la versione contiene misprints, ma non la modifico piu' almeno gli studenti possono stampare definitivamente



Teaching Material (in alphabetic order)


·         M. Atiyah , I. G. Macdonald : Introduction To Commutative Algebra, Addison-Wesley Series in Mathematics(IN BIBLIOTECA)

·          F. Bottaccin: Introduzione alla Geometria Algebrica, 2010/11

·         C. Ciliberto : Drafts of “Algebraic Geometry” course

·         O. Debarre: Introduction à la géométrie algébrique,e, cours de DEA, 1999/2000, et M2, 2007/2008.

·          I. Dolgachev : Introduction to algebraic geometry, 2013

·         W. E. Fulton : Algebraic Curves. An introduction to algebraic geometry, 2008

·          A. Gathmann: Algebraic Geometry, Notes for a class taught at the University of Kaiserslautern, 2002/03

·         J. Harris : Algebraic geometry (a first course), Graduate Texts in Math. No. 133. Springer, New York-Heidelberg, 1977 (IN BIBLIOTECA)

·         R. Hartshorne : Algebraic Geometry, New York: Springer-Verlag, 1977. (IN BIBLIOTECA)

·         B. Hassett: Introduction to algebraic geometry, Cambridge University Press. 2007 (IN BIBLIOTECA)

·         K. Hulek: Elementary Algebraic Geometry, Student mathematical library, vol. 20. 2003 AMS

·          K. Kendig: "Elementary Algebraic Geometry", Dover Books on Mathematics, second edition, Dover Publications, 2015.

·          J. MIlne : Algebraic Geometry, Notes on-line

·          D. Mumford : "The Red Book of Varieties and Schemes", LNM 1358, Springer (IN BIBLIOTECA)

·          M. Reid : Undergraduate Algebraic Geometry, London Math. Soc. Student Texts, vol. 12, 1988, Cambridge University Press

·          I. Shafarevich : Basic Algebraic Geometry, I. Springer-Verlag, New York-Heidelberg, 1977. (IN BIBLIOTECA)

·         E. Sernesi : Private Notes "Algebraic Geometry Course".

·         E. Sernesi : "Appunti sui divisori speciali", typewritten handouts.

·          E. Sernesi : "Una breve introduzione alle curve algebriche", Atti Convegno Geometria Algebrica, Genova-Nervi 1984, 7-38:Scanned pdf

and translation in english (update by C. Fontanari)

·          K. Ueno: An Introduction to Algebraic Geometry (Translations of Mathematical Monographs) 1997. (IN BIBLIOTECA)

·          A. Verra : Introduzione alle curve algebriche piane, Alfaclass Summer School



Something about Algebraic Geometry


·         Geometria Algebrica

·         Algebraic Geometry

·         G. Castelnuovo

·         F. Enriques

·         G. Fano

·         A. Grothendieck

·         D. Hilbert

·         E. Noether

·         M. Noether

·          C. Segre

·          J.P. Serre

·          F. Severi

·          G. Veronese

·          A. Weil

·          O. Zariski



Exams/Learning aims


* Exam Oral examination


* Learning aims Our general scope is to present fundamental concepts related to the problem of solvings systems of polynomial equations. Algebraic Geometry studies these solutions from a “global” point of view, through the theory of Algebraic Varieties. We will define this important class of varieties and then we will study some of their most important properties and discuss key examples, which are fundamental for the whole theory. Learning aims are to give to students the following skills:

·         working knowledge of basic elements of affine/projective geometry, of homomorphisms, isomorphisms and rational maps among algebraic varieties;

·         familiarity with explicit examples, including plane curves, quadric surfaces, Grassmannian of lines, Veronese and Segre varieties, etc;

·         if time permits, familiarity with the rich geometry of the canonical curve in terms of special linear series.


Exams: date/room/hours

o 1o Exam: June 22, 2015, Room 16, Hour from 09-30 a.m.

o 2o Exam: July 10, 2015, Room 11, Hour from 10-00 a.m.

o 3o Exam: September 23, 2015, Room 29A, Hour from 10-00 a.m.

o 4o Exam: January 20, 2016, Room 29A, Hour from 10-00 a.m.


Some of the past years

Prof. G. Pareschi a.a.2012-2013

Prof. C. Ciliberto a.a.2010/11 & 2011/12

Prof.ssa F. Tovena a.a.2009-2010