University of Warsaw - Central Authentication System

Algebraic Geometry

General data

Course ID:	1000-135GEA
Erasmus code / ISCED:	11.163 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Algebraic Geometry
Name in Polish:	Geometria algebraiczna
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	6.00 Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective courses
Requirements:	Algebraic methods in geometry and topology 1000-135MGT Commutative algebra 1000-135ALP
Prerequisites:	Algebra I 1000-113aAG1a
Prerequisites (description):	(in Polish) Wymagane: Algebra przemienna, Metody algebraiczne geometrii i topologii, zalecane: Geometria różniczkowa, Algebra 2, Topologia 2, Funkcje analityczne. Inne przedmioty fakultatywne związane z wykładem: Topologia algebraiczna, Analiza zespolona, Geometria różniczkowa 2, Grupy i algebry Liego.
Short description:	This is an introductory course in algebraic geometry. The aim is to introduce students to algebraic varieties and their basic geometric properties. At the end of the course examples of applications of algebraic geometry will be shown.
Full description:	Algebraic properties of rings and the field of rational functions. Algebraic subsets of affine and projective spaces. Regular mappings. Rational and bi-rational maps. Segre embeddings. Local rings of functions. Tangent and co-tangent spaces. Algebraic theory of local rings. Smooth point of algebraic sets. Integral extensions of rings. The dimension of an algebraic set. Normal points and sets.
Bibliography:	D. Eisenbud, J. Harris, The geometry of schemes, Graduate Texts in Mathematics 197, Springer-Verlag, 2000. R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer-Verlag, 1977. K. Hulek, Elementary algebraic geometry, Student Mathematical Library 20, American Mathematical Society, 2003. D. Mumford, Algebraic geometry I: Complex projective varieties, Classics in Mathematics, Springer-Verlag, 1995. M. Reid, Undergraduate algebraic geometry, London Mathematical Society Student Texts 12, Cambridge University Press, 1988. I. R. Shafarevich, Basic algebraic geometry 1, 2, 2nd ed., Springer-Verlag, 1994.
Learning outcomes:	A student should be able to: - formulate notions from the syllabus and explain them in examples - formulate theorems from the syllabus and give some chosen proofs
Assessment methods and assessment criteria:	The final mark will be given on basis of the results of exercises and the final exam. Detailed rules for completing the course are provided in the information on classes in the relevant academic year.

Classes in period "Summer semester 2023/24" (in progress)

Time span:	2024-02-19 - 2024-06-16	Selected timetable range: weekly course term Navigate to timetable MO TU WYK CW W TH FR
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Adrian Langer
Group instructors:	Adrian Langer
Students list:	(inaccessible to you)
Examination:	Course - Examination Lecture - Examination

Classes in period "Summer semester 2024/25" (future)

Time span:	2025-02-17 - 2025-06-08	Selected timetable range: weekly course term Navigate to timetable
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Agnieszka Bodzenta-Skibińska
Group instructors:	Agnieszka Bodzenta-Skibińska, Francesco Galuppi
Students list:	(inaccessible to you)
Examination:	Course - Examination Lecture - Examination

Course descriptions are protected by copyright.
Copyright by University of Warsaw.