Organizers: Suraj Dash and Khai-Hoan Nguyen-Dang
Time: Saturday at 16:00 CEST via Zoom. The first talk will take place on October 2.
The first part of the seminar covers the basic language of Log Geometry based on [OG] Ogus' Lectures on Logarithmic Algebraic Geometry.
Other useful references are [MG] Mark Gross' Tropical Geometry and Mirror Symmetry for more examples and [OL] Martin Olsson's Logarithmic Geometry and Algebraic Stacks for a complement.
Overview and Planning.
Geometry of Monoids. [OG, I.1.1-1.5]
Functority of Log Schemes. [OG, III.1.1-1.3]
Charts of Log Schemes. [OG, III.1.4]
’Étale log structures’ ⇐⇒ ’Zariski Log structures’. [OL1, ??]
Geometry of Monoids II. [OG, I.4.1,4.2,4.5,4.6,4.8]
Morphisms of Log Schemes. Fiber Products of Log Schemes [OG, II.2]
Theory of "neat" Charts. [OG, II.2.3] and [OL1, ??]
’Log Geometry’ ⇐⇒ ’Toric Varieties’. [MG, ??]
Deligne-Falting Structure. [OG, II.1.6-1.7]
’Log Structures’ ⇐⇒ ’Morphisms of Certain Line Bundles’
Log Derivations and Log Differentials. [OG, IV.1-2]
Log Smoothness (Étale, Unramified,..). [OG, IV.3.1] + [MG]
Kato’s Criterion for Log Smoothness. [OG, IV.3.2]
Other Criterions. [OG, IV.3.3]
Log Flatness. [OG, IV.4] + [OL, ??]
Log Deformation Theory. [OG, III.4]
Log de Rham Cohomology. [OG, IV]+[MG, III.5]