Program - December 20, 2021 (Aula Dottorato, first floor)
You can download the poster and the program.
14:00-14:50
Francesco Denisi
Boucksom-Zariski chambers, volumes, and Newton-Okounkov-type bodies on hyperkähler manifolds.
Abstract:
In this talk I will provide for the big cone of a projective hyperkähler
manifold a decomposition into chambers, in each of which the support
of the negative part of the Boucksom-Zariski decomposition is constant.
I will show how the obtained decomposition allows to determine the
volume function. To conclude, time permitting, I will associate to any big
divisor a 2-dimensional convex body, whose (euclidean) geometry is
strictly related to both the volume and the variation in the big cone of the
divisor itself.
15:00-15:50
Luca Giovenzana
Singularities of the perfect cone compactification
Abstract:
The search for compactifications of moduli spaces is a central problem
in algebraic geometry. Toroidal compactifications were constructed by
Mumford to compactify moduli spaces that are locally symmetric
varieties. In particular they define compactifications of the moduli space
of polarised K3 surfaces with ADE singularities. After recalling the main
properties of toroidal compactifications I will present some results
about the singularities of a specific one, called perfect cone
compactification.
16:30-17:20
Elisa Lorenzo Garcia
Reduction type of
hyperelliptic curves in
terms of the valuations of
their invariants.
Abstract:
In this talk we will first review the classical criteria to determine the
(stable) reduction type of elliptic curves (Tate) and of genus 2 curves
(Liu) in terms of the valuations of some particular combinations of their
invariants. We will also revisit the theory of cluster pictures to determine
the reduction type of hyperelliptic curves (Dokchitser's et al.). Via
Mumford theta constants and Takase and Tomae's formulas we will be
able to read the cluster picture information by looking at the valuations
of some (à la Tsuyumine) invariants in the genus 3 case. We will also
discuss the possible generalization of this strategy for any genus and
some related open questions.
This event is supported by the reasearch project ERC-2017-CoG-771507, StabCondEn (
web page).