Lecturer: Miles Reid
Term: Term 2, that is, 10 weeks 11th Jan-Fri 19th Mar 2021
Commitment: 30 lectures. Provisional timetable: Mon 16:00, Thu 12:00, Fri 10:00
on Teams (email me to sign up).
More: See my MA940 webpage for more material, including videos of past lectures
Assessment: Oral exam (only available for credit to UoW PhD students)
Prerequisites: See below
Content: The main trunk of the lecture course is the classic:
[FAC] Jean-Pierre Serre, Faisceaux algébriques cohérents
Annals of Mathematics (2) 61:2 (1955) 197-278.
Download it from JSTOR https://www.jstor.org/stable/1969915
There is even an English translation for the less pretentious.
Serre's classic paper is to some extent dated, although the historical context
is valuable, as I will discuss. Hartshorne's book (appearing 20 years later) has
some technical improvements, but has its own difficulties for the beginning
student. I adopt Serre's paper as the main trunk, to build the subject on the
simplest possible foundations, with many side branches treating different points
of view: some historically important, providing intuitive alternatives to
illustrate the bigger picture, relating the material to other branches of
geometry, or (as time allows) going further into foundational points or
A light-weight treatment of many of the ideas of the course is contained in
Chapter B of my Park City Chapters on Algebraic Surfaces. My intention there was
a colloquial summary of the theory and how to use it, rather than any systematic
development of the material. I consider it reasonable to assume that any student
interested in this module will be willing to skim through my Chapter B to get
the flavour of the material.
References: Robin Hartshorne, Algebraic geometry, Graduate Texts, Springer, 1977.
(Warwick library e-book: http://webcat.warwick.ac.uk/record=b3214992~S1)
Ravi Vakil, The Rising Sea: Foundations of Algebraic Geometry,
Miles Reid, Chapters on algebraic surfaces, in Complex algebraic geometry
(Park City, UT, 1993), 3-159 (1997). Printout will be available from shelves
outside B2.30. The preprint arXiv: alg-geom/9602006 is on my website (but
the published version is nicer to read).
If time allows, I may also cover the key papers
Armand Borel and Jean-Pierre Serre, Le théorème de Riemann-Roch, Bull.
Soc. Math. France 86 (1958), 97-136
Alexander Grothendieck, La théorie des classes de Chern, Bull. Soc. Math.
France 86 (1958), 137–154
See also Raoul Bott's detailed review MR0116022 (22 #6817 and #6818)