The Riemann-Roch in Log Geometry
開催期間
16:00 ~ 17:30
場所
講演者
概要
【講演要旨】 For log smooth fibrations of log smooth varieties,
we investigate how the Grothendieck-Riemann-Roch theorem
applies. With the help of relative logarithmic tangent bundles
and a new type of genus, the GRR now stands as
Coh = Log + Hor + Ver,
with Coh the cohomology part, and
the intersection part naturally decomposes:
Log = contributions from log relative tangent bundle,
Hor = contributions from horizontal divisors, and
Ver = contributions from vertical singularities.
We will use this thm to study stably compactified moduli spaces
of marked curves. In fact, Mumford's related work plays a key role
in our understanding. In addition, we will indicate how such a result
can be applied to study a local family index theorem for log smooth
fibrations, particularly, to the study of relative Bott-Chern secondary
characteristic classes appeared in the arithmetic Grothendiect-Roemann-
Roch.
*幾何学セミナーはグローバルCOEプログラム「マス・フォア・インダストリ」
の活動の一環として行われております。