Schedule

Tuesday

Helge Ruddat - Smoothing singular toric Fanos

This talk provides an overview of Alessio Corti’s contributions, including our joint work, to the program of constructing smoothings for singular toric Fano varieties. A key achievement of this program is the unifying production of all 105 smooth Fano threefolds from singular toric varieties by a single method. The construction of (all?) Q-Gorenstein Fano 3-folds and smooth Fano 4-folds is within reach. I will highlight Alessio’s recent work about zero-mutable Laurent polynomials, explaining their role in constructing log structures and their application to studying the topology of complex singularities, such as the well-known but challenging Tom and Jerry singularities.

Wednesday

Miles Reid - The Tate-Oort group scheme TO_n for n >= 1

We construct the Tate-Oort group scheme TO_n. For the prime case TO_p see https://mreid.warwick.ac.uk/TOp. This is the cyclic group ZZ/n _as you have never seen it before_: it lives over an arithmetic base; over primes not dividing n, it is an etale form of ZZ/n. However, where p^r divides n, its degenerations include the nonreduced group schemes mu_{p^i} and alpha_{p^i} for i < r, alongside etale forms of ZZ/(n/p^r). Our construction is straightforward, based on simple modifications of the celebrated Cauchy-Liouville-Mirimanoff polynomials. Joint with LIAO Yiming.

Friday

Dan Abramovich - Resolution of singularities on foliated orbifolds

We resolve singularities of a subvariety X of a smooth variety Y endowed with a foliation F, through weighted blowups aligned with F. Stacks and logarithmic structures will feature prominently, yet explicitly and concretely, with examples, as befits the event. This is work with A. Belotto da Silva, M. Temkin and J. Włodarczyk. 

Carolina Araujo - Automorphisms of quartic surfaces and Cremona transformations 

In this talk, I will address the following question, attributed to Gizatullin: "Which automorphisms of a smooth quartic surface in projective 3-space are restrictions of Cremona transformations of the ambient space?" Corti and Kaloghiros have introduced a general framework that is extremely useful for approaching this problem, namely, a special version of the Sarkisov program for Calabi-Yau pairs. I will report on recent progress on Gizatullin’s problem obtained using this theory, in collaborations with Alessio Corti and Alex Massarenti, and with Daniela Paiva and Sokratis Zikas.