course: Logarithmic structures with a view towards moduli

speaker: Martin Olsson (UC Berkeley)

abstract: In this mini-course, I have two main aims:

(1) to discuss the basic theory of logarithmic geometry in the sense of Fontaine, Illusie, and Kato, and

(2) illustrate through a number of examples the utility of log structures in the study of moduli spaces. The tentative plan for the lectures is the following.

-- Log structures and log schemes, charts, differentials. -- Log smooth and log étale morphisms. Kato's structure theorem. Log de Rham cohomology. -- Log deformation theory. Log cotangent complex. -- Examples: the Deligne-Mumford compactification of Mg as a moduli space for log curves, local moduli for degenerating K3 surfaces, toric Hilbert scheme, broken toric varieties. -- Connection with stacks. Twisted curves and log geometry.

The main prerequisite for the course, in addition to standard scheme theory and coherent cohomology, is some familiarity with the étale topology of schemes as can for example be found in Milne's book `Étale cohomology'. Students wanting a head start might also consult the article `Logarithmic structures of Fontaine-Illusie', by K. Kato Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), 191--224, Johns Hopkins Univ. Press, Baltimore, MD, 1989.

timetable:
Mon 16 Jun, 17:00 - 18:00, Aula Dini
Tue 17 Jun, 17:00 - 18:00, Aula Dini
Wed 18 Jun, 11:15 - 12:05, Aula Dini
Thu 19 Jun, 17:00 - 18:00, Aula Dini
Fri 20 Jun, 17:00 - 18:00, Aula Dini
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