Subjects

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Algebraic Geometry - NDGE011

Title:	Algebraická geometrie
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2010 to 2013
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time

Guarantor:	doc. RNDr. Leo Boček, CSc.
Teacher(s):	doc. RNDr. Leo Boček, CSc.
Classification:	Mathematics > Geometry

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Annotation -

Forms of n-th degree, algebraic surfaces and their properties - multiple points, polars, tangent planes. Algebraic curves in the plane, theorem of Bezout, Pluckers formulas.

Last update: T_KDM (22.05.2001)

Aim of the course -

This course helps to obtain theoretical background for teaching mathematics at high school.

Last update: T_KDM (19.05.2008)

Literature -

Kočandrle M. Algebraické variety. SPN Praha, 1989.

Švec A. Příklady z algebraické geometrie. SPN Praha, 1970.

Walker R. J. Algebraic Curves. Springer-Verlag, New York, 1950.

Reid M. Undergraduate Algebraic Geometry. Cambridge University Press, 1989.

Last update: T_KDM (13.05.2008)

Teaching methods -

Lectures.

Last update: T_KDM (19.05.2008)

Syllabus -

Algebraic hypersurfaces, reducibility and irreducibility, degree of a hypersurface, regular and singular points, polar of order n, tangent hyperplane and tangent line of a hypersurface.

Planar algebraic curves, determination of an algebraic curve, resultant, theorem of Bezout, bounds for number of singular points of a reducible and irreducible algebraic curve, genus of a curve, parametrization of curves of genus 0, Hessian of a curve, Plucker's formulas.

Last update: T_KDM (28.05.2003)