Conference Shokurov 70+1
May 17-18, 2021
Abstracts of the talks


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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