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London-Tokyo Workshop In Birational Geometry II


Location: Imperial College - Huxley Building

Date: Wednesday, 5 December 2018 - Thursday, 6 December 2018

Organisers: Paolo Cascini, Yoshinori Gongyo and Yusuke Nakamura


  • Weichung Chen (University of Tokyo)
  • Stefano Filipazzi (University of Utah)
  • Naoki Koseki (University of Tokyo/IPMU)
  • Masaru Nagaoka (University of Tokyo)
  • Johannes Nicaise (Imperial College)
  • Kentaro Ohno (University of Tokyo)
  • Christian Urech (Imperial College)


Wednesday, 5 December - Room 140

1:00 - 1:50: Naoki Koseki

2:00- 2:50: Kentaro Ohno

3:30 - 4:20: Weichung Chen

4:30 -5:20: Stefano Filipazzi

Thursday, 6 December - Room 130

10:00 - 10:50 Christian Urech

11:00 - 11:50 Masaru Nagaoka

12:00 - 12:50 Johannes Nicaise

Titles and Abstracts:

Weichung Chen

Title:Boundedness of weak Fano Pairs with alpha-invariants and volumes bounded below 

Abstract:We show that fixed dimensional klt weak Fano pairs with alpha-invariants and volumes bounded away from 0 and the coefficients of the boundaries belong to a fixed DCC set of rational closure form a bounded family. We also show α(X, B)^(d-1)vol(-(K_X + B)) are bounded from above for all klt weak Fano pairs (X, B) of a fixed dimension d.

Stefano Filipazzi

Title: A generalized canonical bundle formula and applications

Abstract: Birkar and Zhang recently introduced the notion of generalized pair. These pairs are closely related to the canonical bundle formula and have been a fruitful tool for recent developments in birational geometry. In this talk, I will introduce a version of the canonical bundle formula for generalized pairs. This machinery allows us to develop a theory of adjunction and inversion thereof for generalized pairs. I will conclude by discussing some applications to a conjecture of Prokhorov and Shokurov.

Naoki Koseki

Title: Stability conditions on threefolds with nef tangent bundles

Abstract:  Constructing Bridgeland stability conditions on threefolds is an open  problem in general.  By the work of Bayer, Macri, and Toda, the problem is reduced to proving  the so-called Bogomolov-Gieseker (BG) type inequality conjecture. In my talk, I will  explain how to solve the BG type inequality conjecture for threefolds in the title. 

Masaru Nagaoka

Title: On compactifications of contractible affine threefolds into del  Pezzo fibrations

Abstract: By the contribution of M. Furushima, N. Nakayama, Th.  Peternell and M. Schneider, it is completed to classify all projective  compactifications of the affine $3$-space $¥mathbb{A}^3$ with Picard  number one. After that, T. Kishimoto observed that their arguments make use of only  the contractibility of $¥mathbb{A}^3$ and that the ambient space are  Fano manifolds. In this talk, I will consider compactifications of contractible affine  threefolds into another special manifolds, i.e. del Pezzo fibrations. Mainly I will introduce a certain type of such compactifications, which  seems to have connection with vertical cylinder, and give you examples  of such certain compactifications.

Johannes Nicaise

Title: Specialization of (stable) rationality in families with mild singularities

Abstract: I will present joint work with Evgeny Shinder, where we use Denef and Loeser’s motivic nearby fiber and a theorem by Larsen and Lunts to prove that stable rationality specializes in families with mild singularities. I will also discuss an improvement of our results by Kontsevich and Tschinkel, who defined a birational version of the motivic nearby fiber to prove specialization of rationality.

Kentaro Ohno

Title: Minimizing CM degree and slope stability of projective varieties

Abstract: We discuss a minimization problem of the degree of the CM line bundle among all possible fillings of a polarized family with fixed general fibers. This problem derives from the study on the compactification of moduli spaces. In this talk, we show that such minimization implies the slope semistability of the fiber if the central fiber is smooth.

Christian Urech

Title: On the characterization of affine surfaces by their automorphism groups

Abstract: In this talk we will look at the question, in as far affine surfaces are  characterized by the group structure of their automorphism groups. In  particular, we will see that if $S$ is a toric surface and $S'$ any  normal affine surface such that $Aut(S)$ and $Aut(S')$ are isomorphic as  groups, then $S$ and $S'$ are isomorphic. The main ingredients of the  proof are results on the degree growth of birational transformations.  This is joint work with Liendo and Regeta.



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