Messages
7.10. Nikolai: Sheaves of differentials
14.10: Martin: Curves on P1xP1
21.10: Edvard: Serre duality on curves
28.10: Jon-Magnus: Linear systems of conics
13.10: Torger Olson: Serre duality on curves (on zoom)
Kristian R
in the course this fall are
Nikolai Thode Opdan and Jon-Magnus Rosenblad.
Kristian R
II.20 1-3 (in [B] ) will be discussed next week.
Also, I recommend R. Vakils notes
http://virtualmath1.stanford.edu/~vakil/02-245/
as supplementary reading in the course.
Kristian R
The exercise V.1.4 in Hartshornes book (lines on a surface in P3) will be discussed next week.
In stead of a compulsory problem set to be handed in, I ask each student to give a 20 min presentation of a topic during a lecture.
Here is a start on a list of topics for compulsory presentation:
-The sheaf of differentials on a variety, and on a subvariety.
-Serre duality on a smooth curve
-Curves on P1xP1
-Linear systems of conics in the plane, and the maps that they define (describe fibers and image)
to be extended..
Kristian R
Sept 1-2 Linear systems on curves (EO 17.4, 20.1, 20.3, 20.4)
Sept 8-9 Picard group and RR for surfaces (B ch 1)
Sept 15-16 Birational maps (B ch 2)
etc
approximately one chapter in B each week until ch 10.
There may be some interruptions, I plan for student presentations as compulsory exercises.
Kristian R
Allthough Beauvilles book will contain the major part of the material for the course, I will use some material from Hartshornes book, but probably even more from the "Introduction to Schemes" by Ellingsrud and Ottem (EO).
In my first couple of weeks I will cover material from EO:
12.3 Linear systems + 15.1-2 Morphisms to projective space
15.6 Serre's theorems and Euler characteristic
17. 1-4 Curves + 19.1 (Easy) Riemann Roch for curves
Kristian R
Emnet dette semesteret vil dreie seg om komplekse algebraiske flater, klassifikasjon og eksempler. Som en oppvarming vil jeg begynne med kurver. Presentasjon og resultater vil i hovedsak hentes fra Beauvilles bok "Complex algebraic surfaces" (original fransk utgave) og Hartshornes bok "Algebraic geometry".
F?rste forelesning er tirsdag 25. august, vel m?tt!
Kristian R