Boundedness and Moduli Problems in Birational Geometry and Foliation Theory‏

Contribution List

3. Fano 4-folds with large Picard number and blow-ups of cubic 4-folds

Cinzia Casagrande (Università di Torino)

27/10/2025, 09:30

We will present some classification results for (smooth, complex) Fano 4-folds X with Picard number rho(X)>6. First of all, if rho(X)>9, then X is a product of del Pezzo surfaces; this is sharp, since we know one family of Fano 4-folds with rho(X)=9 that is not a product of surfaces. In the range rho(X)=7,8,9, we will explain some partial classification results, based on a detailed and...

14. Rational curves on very general complete intersections of high degree.

Gianluca Pacienza (Université de Lorraine)

27/10/2025, 11:00

I will report on a joint work-in-progress with F. Bastianelli. It is well known thanks to Ein that very general complete intersections of multidegree (d_1,…,d_c) in the projective n-space do not contain rational curves as soon as d_1+…+d_c > 2n-c-1. This result has been sharpened in the case of hypersurfaces thanks to a method introduced by Voisin that inspired further work by Clemens, Ran and...

4. The cone conjecture for various finite quotients

Cecile Gachet (Ruhr-Universität Bochum)

27/10/2025, 14:30

The cone conjecture predicts the shape of the nef and movable cones of certain projective varieties, modulo automorphisms. It is notably known for K3 surfaces, abelian varieties, hyperkähler manifolds, and in a few sporadic cases. Together with standard MMP conjectures, it implies the finiteness of minimal models, which can be used to improve birational boundedness to boundedness for certain...

6. Moduli of surface foliations

Calum Spicer (King's College, London)

28/10/2025, 09:30

I will report on some recent progress on the construction of a moduli space of surface foliations of general type. Time permitting I will also discuss some aspects of this moduli problem in general, as well as appliclations to the construction of moduli of fibred varieties. This talk will partly cover joint work with S. Velazquez and R. Svaldi.

8. On the birational geometry of algebraically integrable foliations

Paolo Cascini

28/10/2025, 11:00

I will review recent progress on extending the Minimal Model Program to foliations. Building on techniques from both birational geometry and the theory of foliations, we obtain new results on the structure of foliated pairs. I will focus on applications such as the boundedness of algebraically integrable Fano foliations. Joint work with Han, Liu, Meng, Spicer, Svaldi, and Xie.

9. On the boundedness of algebraically integrable foliations of general type

Jihao Liu (Peking University)

28/10/2025, 14:30

I shall discuss recent ongoing work on the boundedness of algebraically integrable foliations of general type based on the theory of adjoint foliated structures. In particular, I will discuss a birational boundedness theorem that builds on the proof of McKernan’s ACC conjecture for interpolated log canonical thresholds for algebraically integrable foliations.

12. Semiampleness of line bundles arising from Hodge theory

Mirko Mauri (CNRS)

29/10/2025, 09:30

Semiampleness criteria are subtle foundational statements in algebraic geometry. In this talk, we present a new semiampleness result for the Hodge bundle of certain Calabi–Yau variations of Hodge structure. This result is a key ingredient in the proof of two long-standing conjectures: Griffiths' conjecture on functorial compactifications of images of period maps, and the b-semiampleness...

10. A proof of the b-semiampleness conjecture

Stefano Filipazzi (Duke University)

29/10/2025, 11:00

A family of Calabi–Yau varieties (or, more generally, log Calabi–Yau pairs) f:X->Y naturally induces a moduli divisor M, measuring the variation of the family f. Based on earlier works of the Japanese school, Prokhorov and Shokurov conjectured that M is semiample. In this talk, we discuss a proof of this conjecture and, time permitting, some immediate applications in birational geometry. In...

1. On K3 surfaces with non-elementary hyperbolic automorphism group

Prof. Keiji Oguiso (the University of Tokyo)

29/10/2025, 12:15

My talk is based on my joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjing University).

Main result of my talk is the finiteness of the N\'eron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic under the assumption that the Picard number greater than or equal to 6 which is optimal to ensure the...

2. Blowups, Gale duality and moduli spaces.

Araujo Carolina (IMPA)

30/10/2025, 09:30

In this talk, we discuss the birational geometry of blowups of projective spaces at points in general position. For that, we explore Gale duality -- a correspondence between sets of $n=r+s+2$ points in projective spaces $\mathbb{P}^s$ and $\mathbb{P}^r$. For small values of $s$, this duality has a remarkable geometric manifestation: the blowup of $\mathbb{P}^r$ at $n$ points can be realized as...

15. When Kupka Meets Reeb

Jorge Vitório Pereira (IMPA)

30/10/2025, 11:00

Reeb’s local and global theorems are classical results in the theory of smooth foliations, giving conditions under which a foliation is locally or globally the pullback of a foliation by points. These results depend on assumptions such as compactness and the finiteness of the fundamental group or holonomy of a leaf. In contrast, the Kupka Theorem concerns the local study of singular foliations...

5. Primitive Enriques varieties

Zhixin Xie (Université de Lorraine)

30/10/2025, 14:30

The notion of an Enriques manifold was introduced by Oguiso-Schröer as a complex manifold which is not simply connected and whose universal covering is an irreducible symplectic manifold. From the viewpoint of birational geometry, we want to understand its behaviour under Minimal Model Program (MMP) operations. Based on the result of Lehn-Pacienza showing that any MMP starting from a primitive...

11. Boundedness of Polarized Log Calabi–Yau Fibrations with Bounded Bases

Xiaowei Jiang (Tsinghua University)

31/10/2025, 09:30

In this talk, we discuss the boundedness problem for log Calabi–Yau fibrations whose bases and general fibers are bounded. We show that, after fixing certain natural invariants, the total spaces of such fibrations are bounded in codimension one. Furthermore, we prove that the total spaces themselves are bounded when the general fibers have vanishing irregularity. As an application, we obtain...

7. A tale of three GIT problems.

Aline Zanardini (EPFL)

31/10/2025, 11:00

In this talk, I will report on work in progress, joint with M. Hattori and T. Papazachariou, concerning a classical cycle of correspondences among (particular) nets of quadrics in P3, nets of cubics in P2, and (smooth) plane curves ofdegree four. I will explain how, by extending these correspondences, one can obtain precise links among the three corresponding GIT problems.