Subjects

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Algebraic Geometry - NMUG403

Title:	Algebraická geometrie
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	winter
E-Credits:	2
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
Teaching methods:	full-time

Guarantor:	RNDr. Jana Hromadová, Ph.D.
Classification:	Mathematics > Geometry
Incompatibility :	NMTD403
Interchangeability :	NMTD403
Is incompatible with:	NMTD403
Is interchangeable with:	NMTD403

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Annotation -

Last update: T_KDM (04.05.2015)

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.

Aim of the course -

Last update: T_KDM (04.05.2015)

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

Course completion requirements -

Last update: RNDr. Jana Hromadová, Ph.D. (28.10.2019)

The course is completed by an exam. The exam is written, it will contain numerical and theoretical questions. If the written part will be passed / failed, the oral examination will follow. Oral examination may also be carried out to clarify or explain the unclear parts of the written test.

The student is entitled to have one regular and two retake exams.

Literature -

Last update: T_KDM (04.05.2015)

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.

Teaching methods -

Last update: T_KDM (04.05.2015)

Lectures.

Requirements to the exam -

Last update: RNDr. Jana Hromadová, Ph.D. (28.10.2019)

The examination requirements correspond to the syllabus of the subject given in the SIS.

Syllabus -

Last update: T_KDM (04.05.2015)

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.