Log Seminar

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.

Tentative Schedule

Talk 0

  • Overview and Planning.

Talk I

  • Geometry of Monoids. [OG, I.1.1-1.5]

Talk II

  • 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, ??]

Talk III

  • 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]

Talk IV

  • Theory of "neat" Charts. [OG, II.2.3] and [OL1, ??]

  • ’Log Geometry’ ⇐⇒ ’Toric Varieties’. [MG, ??]

Talk V

  • Deligne-Falting Structure. [OG, II.1.6-1.7]

’Log Structures’ ⇐⇒ ’Morphisms of Certain Line Bundles’

Talk VI

  • Log Derivations and Log Differentials. [OG, IV.1-2]

  • Log Smoothness (Étale, Unramified,..). [OG, IV.3.1] + [MG]

Talk VII

  • Kato’s Criterion for Log Smoothness. [OG, IV.3.2]

  • Other Criterions. [OG, IV.3.3]


  • Log Flatness. [OG, IV.4] + [OL, ??]

Talk IX

  • Log Deformation Theory. [OG, III.4]

Talk X

  • Log de Rham Cohomology. [OG, IV]+[MG, III.5]