2013/2014

2014/2015

DM270

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

2°

2nd semester (02/03/2015 - 12/06/2015)

9

72 lesson hours

ITALIAN

ORAL TEST

PIROLA GIAN PIETRO (titolare) - 6 ECTS
FREDIANI PAOLA - 3 ECTS

The contents of the courses Algebra 1, Geometry 1 and 2, Linear Algebra, and of the courses in Analysis of the first two years in maths courses

The course intends to give an introduction to the
basic concepts and methods of differential Geometry

Differentiable varieties, Elements of differentiable topology,Riemannian Geometry,Complex and Algebraic varieties.

Extended summary

Differentiable varieties:
Tangent and cotangent spaces, vector fields and forms. Froebenius theorem, Lie groups and Lie algebras.

Elements of differentiable topology:
Sard lemma , De Rahm theorem

Riemannian Geometry:
Riemannian varieties, Levi Civita connection,
curvature, geodesics, Hopf-Rinow and Whithehead thorems, Jacobi fields.

Complex and Algebraic varieties.
Holomorphic and meromorphic functions, Kaeheler and projective varieties. Zariski topology

Lectures

Gian Pietro Pirola: dispense.
Frank Warner: "Foundations of differentiable manifolds and Lie groups".
Graduate Texts in Mathematics, 94. Springer-Verlag, New York-Berlin.
Manfredo Perdigao Do Carmo: "Riemannian Geometry", Birkhaeuser.
Boothby, William M.: "An introduction to differentiable manifolds and
Riemannian geometry". Pure and Applied Mathematics, No. 63. Academic Press,
New York-London, 1975.
Th. Broecker and K. Jaenich: "Introduction to differential topology".
Milnor, J.: "Morse theory". Annals of Mathematics Studies, No. 51 Princeton
University Press, Princeton, N.J. 1963.
D. Huybrechts: "Complex geometry. An introduction". Universitext.
Springer-Verlag, Berlin, 2005.
P.A. Griffiths, J. Harris: "Principles of algebraic geometry". John Wiley &
Sons, Inc., New York, 1994. Wiley & sons.
I.R. Shafarevich: "Basic Algebraic Geometry 1" (Second Edition), Springer, 1994.
J. Harris, "Algebraic Geometry - A First Course", Graduate Texts in Mathematics 133,
Springer, 1992.

Oral examination

Oral examination