(in Polish) Zaawansowane narzędzia geometrii algebraicznej

General data

Course ID:	1000-1M21ZNG
Erasmus code / ISCED:	11.1 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:	(unknown)
Name in Polish:	Zaawansowane narzędzia geometrii algebraicznej
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):	(not available) 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 monographs
Short description:	our aim is to introduce, prove and apply classical yet difficult theorems of algebraic geometry, such as Zariski's Main Theorem, cohomology and base change, vanishing theorems.
Full description:	The first half will roughly consist of (1) recap about flat and smooth morphisms, (2) cohomology and base change theorem and applications, (3) the theorem on formal function, Zariski's Main Theorem and Stein factorization (4) Serre's duality and applications, (5) Kodaira's vanishing theorem. The second half will consists of participants' choices among several possible directions (e.g. Artin's approximation or introduction to stacks).
Bibliography:	given at the homepage. In the first half, we will follow R. Vaki's "Foundations of algebraic geometry"
Learning outcomes:	the student knows the above mentioned theorems and is able to apply them in nontrivial situations, appropriately modifying the assumptions.
Assessment methods and assessment criteria:	a part of the exercise sessions will be devoted to attendies' lectures. The final grade will depend on those and on the final oral exam.

This course is not currently offered.

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