Constructions and obstructions in birational geometry

5-9 November 2018

ICMS, The Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT

Scientific Organisers

  • Arend Bayer, University of Edinburgh
  • Ivan Cheltsov, University of Edinburgh
  • Liana Heuberger, University of Warwick
  • Evgeny Shinder, University of Sheffield

This timely workshop focuses on the fast-developing field of Birational Geometry. Bringing together some of the most well-known algebraic geometers in recent times, the aim of the workshop includes reviewing the most important recent developments in birational geometry, relating to the explicit methods and toric varieties and degenerations on the Constructions side, and Chow groups, derived categories and the Grothendieck ring of varieties on the Obstructions side, and subsequently initiating the discussion between experts. The chosen themes cover a broad spectrum of research currently being carried out in birational geometry, both by UK-based mathematicians and by their international collaborators.  The workshop is dedicated William Edge, born on November 8th, 1904, who pioneered research in Algebraic Geometry in Britain and worked at the University of Edinburgh for most of his life.

Full details on how to participate in the workshop will appear here shortly.

Speakers

The organisers are delighted to announce that Claire Voisin, Collège de France, will participate in the conference and we are grateful to the Clay Mathematical Institute for their generous support which has made this possible. Claire Voisin is widely recognised as one of the most remarkable and stimulating mathematicians of our time. 

Confirmed Speakers

Hamid Ahmadinezhad, Loughborough University
Ekaterina Amerik, Université de Paris-Sud
Arnaud Beauville Université de Nice Sophia Antipolis
Lev Borisov, Rutgers University
Cinzia Casagrande, Università degli Studi di Torino
Jean-Louis Colliot-Thelene, Université Paris-Sud
Alessio Corti Imperial College London
Enrica Floris University of Basel
Sergey Gorchinskiy, Steklov Mathematical Institute
Anne-Sophie Kaloghiros, Brunel University
Alexander Kuznetsov, Steklov Mathematical Institute
Diane MacLagan, University of Warwick
J.C. Ottem, University of Oslo
Rita Pardini, University di Pisa
Marta Pieropan, Free University of Berlin
Piotr Pokora, Pedagogical University of Cracow
Elisa Postinghel, Loughborough University
Constantin Shramov, Steklov Mathematical Institute
Jenia Tevelev, University of Massachusetts
Susanna Zimmerman., Université d'Angers

Arrangements

It is anticipated that the workshop will commence with Registration early on the morning of Monday 5 November and finish around lunchtime on Friday 9 November 2018. Please take this into consideration when making your travel arrangements.

Registration fee

There will be no registration fee for this workshop.

Invitations

Invited speakers were sent an invitation on Monday 6 August from ICMS by email. All other participants are invited to apply to this workshop by public application form which will be available on this website shortly. For PhD student applicants, a reference letter from their supervisor will be expected.

UK Visas

If you are travelling from outside of the UK you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one.

Travel

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

A taxi directly from the airport will cost approximately 20.00 to 25.00 GBP to the city centre for a one-way journey. 
There is also a bus service direct from the airport to the city centre which will cost 4.50 GBP single or 7.50 GBP return - the Airlink 100. This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station, only a short walk to the workshop venue.
Lothian buses charge £1.70 for a single, £4.00 for a day ticket. Please note that the exact fare is required and no change is given.
If travelling by train, please note that Edinburgh has several railway stations - Waverley Railway Station being the main station and closest to the workshop venue. If you alight at Edinburgh Waverley, the workshop venue is an easy 15 minute walk away

Programme

A tentative programme will be appear here shortly.

 

Talks and abstracts

Alessio Corti
Volume-preserving birational maps of PP3
After a short summary of the Sarkisov program for Mori fibred Calabi–Yau pairs, I report on joint work with Araujo and Massarenti on volume preserving birational maps of PP3.

Anne-Sophie Kaloghiros
Maximal intersection Calabi-Yau pairs
A Calabi-Yau (CY) pair (X, D) consists of a normal projective variety and a reduced
anti-canonical integral divisor D on it. Such pairs come up in a variety of contexts; for example, cluster varieties are obtained by glueing CY pairs by crepant birational maps. Recent developments in mirror symmetry suggest that cluster varieties are “natural" mirror partners of Fano varieties with a toric degeneration, and that understanding the birational geometry of CY pairs is an important step in the study of mirror symmetry and moduli of Fano varieties.
In this talk, I will discuss the birational geometry of CY pairs and some 3-fold examples.

John Ottem                     
The integral Hodge conjecture for curve classes
The Hodge conjecture predicts which rational cohomology classes on a smooth complex projective variety can be represented by linear combinations of complex subvarieties. The integral Hodge conjecture, the analogous conjecture for integral homology classes, is known to be false in general (the first counterexamples were given in dimension 7 by Atiyah and Hirzebruch). I'll give a short survey talk on this conjecture, and present some new counterexamples in dimension three. This is joint work with Olivier Benoist.

Piotr Pokora
On the bounded negativity conjecture
The main aim of my talk is to present some recent developments on the bounded negativity conjecture. The conjecture states that for every smooth complex projective surface $X$ there exists an integer $b(X)$ such that for all irreducible and reduced curves $C \subset X$ one has $C^{2} \geq -b(X)$. There are some surfaces for which the BNC holds, for instance surfaces with the canonical divisor $-K_{X}$ being $\mathbb{Q}$-effective, but in general the question is open. It is notoriously difficult to predict where a certain blowing up of a given surface has bounded negativity, for instance it is not known whether the blowing up of the complex projective plane along $10$ very general points has bounded negativity. In my talk I am going to discuss the current state of the art in that field especially focusing on the effective bounds on the self-intersection numbers of certain classes of curve on blow ups of surfaces with Kodaira dimension $\leq 0$.

Konstantin Shramov
Birational automorphisms of surfaces and threefolds
I will survey boundedness results for finite groups of birational automorphisms of surfaces and threefolds, with special regard for Jordan property.

Francesco Zucconi
Rationality of special subloci in the moduli space of spin curves
We will show how to use the birational geometry of some well-known Fano 3-folds to prove the rationality of the moduli space of spin hyperelliptic curves and of genus 4 spin curves with a unique trigonal series.