Homogeneous coordinates, projective spaces, the principle of duality, projective planes and the configurations of Desargues and Pappus, collineations and correlations, perspectivities, the projective groups, polarities, algebraic varieties, classical polar spaces, Plücker coordinates, the Klein quadric, Segre varieties, Veronese varieties.

### Projective Geometry (MATH 526)

__here__to view.

Programs\Type | Required | Core Elective | Area Elective |

MA-European Studies | |||

MA-European Studies-Non Thesis | |||

MA-Political Science | |||

MA-Political Science-Non Thes | |||

MA-Visual Arts&Vis. Com Des-NT | |||

MA-Visual Arts&Visual Com Des | |||

MS-Bio. Sci. & Bioeng. LFI | |||

MS-Bio. Sci. & Bioeng. LFI-ENG | |||

MS-Biological Sci&Bioeng. | * | ||

MS-Computer Sci.&Eng. LFI | |||

MS-Computer Sci.&Eng. LFI-ENG | |||

MS-Computer Science and Eng. | * | ||

MS-Cyber Security(with thesis) | * | ||

MS-Data Science | |||

MS-Elec. Eng&Comp Sc.LFI-ENG | |||

MS-Electronics Eng&Comp Sc.LFI | |||

MS-Electronics Eng&Computer Sc | * | ||

MS-Electronics Eng. | * | ||

MS-Electronics Eng. LFI | |||

MS-Electronics Eng. LFI-ENG | |||

MS-Energy Techno.&Man. | * | ||

MS-Industrial Eng. LFI-ENG | |||

MS-Industrial Engineering | * | ||

MS-Industrial Engineering LFI | |||

MS-Manufacturing Eng-Non Thes | * | ||

MS-Manufacturing Engineering | * | ||

MS-Materials Sci & Engineering | * | ||

MS-Materials Sci. & Eng. LFI | |||

MS-Materials Sci.&Eng. LFI-ENG | |||

MS-Mathematics | |||

MS-Mechatronics | * | ||

MS-Mechatronics LFI | |||

MS-Mechatronics LFI-ENG | |||

MS-Physics | |||

MS-Physics-Non Thesis | * | ||

MS-Psychology | |||

MS-Psychology-Non Thesis | |||

PHD-Biological Sci&Bioeng. | * | ||

PHD-Comp. Sci and Eng.after UG | * | ||

PHD-Computer Science and Eng. | * | ||

PHD-Cyber Security | * | ||

PHD-Electronics Eng&ComputerSc | * | ||

PHD-Electronics Eng. | * | ||

PHD-Electronics Eng. after UG | * | ||

PHD-Experimental Psychology | |||

PHD-Industrial Engineering | * | ||

PHD-Management | |||

PHD-Manufacturing Eng after UG | * | ||

PHD-Manufacturing Engineering | * | ||

PHD-Materials Sci.&Engineering | * | ||

PHD-Mathematics | |||

PHD-Mechatronics | * | ||

PHD-Mechatronics after UG | * | ||

PHD-Physics | |||

PHD-Physics after UG | |||

PHD-Social Psychology | |||

PHDBIO after UG | * | ||

PHDCYSEC after UG | * | ||

PHDEECS after UG | * | ||

PHDEPSY after UG | |||

PHDIE after UG | * | ||

PHDMAN after UG | |||

PHDMAN after UG-Finance | |||

PHDMAN after UG-Man. and Org. | |||

PHDMAN after UG-Op.&Sup. Cha. | |||

PHDMAN-Finance Area | |||

PHDMAN-Man. and Org. Area | |||

PHDMAN-Op. & Supp. Chain Area | |||

PHDMAT after UG | * | ||

PHDMATH after UG | |||

PHDSPSY after UG |

### CONTENT

### LEARNING OUTCOME

By the end of the course the students

1. should be able to work with homogeneous coordinates, quotient spaces, and projections in projective spaces,

2. explain and apply the principle of duality, and reproduce the definitions of collineations, correlations, elations, homologies, perspectivities,

3. should be able to state and prove the Fundamental Theorem of Projective Geometry,

4. should be able to work with the action of the classical groups on projective and polar spaces,

5. should be able to state and prove the classical theorems of Desargues and Pappus for projective planes over fields,

6. should be able to give examples non-Desarguesian projective planes,

7. should be able to state and prove combinatorial properties for finite projective planes,

8. should be able reproduce the coordinatization method for projective planes, explain the connection between the algebraic structures of ternary rings (in particular quasifields, semifields, nearfields, division rings, skewfields) and the geometric and group theoretic properties of the corresponding projective planes (in particular, the different types of translation planes),

9. should also be able to define the basic concepts related to the study of algebraic varieties in affine and projective spaces, give the classification of sesquilinear and quadratic forms and the connection with quadratic and hermitian varieties in projective spaces as well as their relation with the classical groups; define the Klein correspondence and the Klein quadric, the Segre variety and the Veronese variety.