Caucher Birkar
Stable minimal models.
In this talk I will introduce the notion of a stable minimal model and give some examples. Next I will discuss their moduli spaces.
János Kollár
Openness of projectivity.
Slides
Alexander Kuznetsov
Categorical absorption of singularities and nodal nonfactorial Fano
threefolds.
If X is a threefold with a nonfactorial ordinary double point, we show that there is a semiorthogonal decomposition of the derived category of X with two components, a "small" component responsible for the singularity (we say it "absorbs" the singularity of the derived category of X), and a "big" component that deforms to the derived category of a smoothing of X. We use this construction to relate the derived categories of Fano threefolds of index 2 and degree d to derived categories of Fano threefolds of index 1 and genus g = 2d + 2. This is joint work in progress with Evgeny Shinder.
James McKernan
Foliations from the view point of Mori theory
We describe some recent work of Paolo Cascini, Calum Spicer
and Roberto Svaldi on foliations on projective varieties. Using ideas
and techniques from Mori theory, especially the idea of using log
pairs, they are able to give a birational classification of foliations
and prove some conjectures on holomorphic foliations.
Dmitri Orlov
Geometric realizations, gluings, and birational geometry.
Vyacheslav Shokurov
Moduli part of adjunction.
Positivity properties and birational
invariance of the upper maximal moduli part
of adjunction will be discussed.
David Villalobos-Paz
Rational curves on algebraic spaces.
In this talk, I will explain a projectivity criterion for proper
algebraic spaces in terms of rational curves. The proof of this
criterion hinges on being able to run a relative MMP in which the base
is an algebraic space.
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