Fano Varieties in Stavanger

Contribution List

8. Singular Log Structures and Fano Threefolds

Prof. Alessio Corti

4/2/25, 9:30 AM

We introduce a class of singular log schemes in 3-dimensions and conjecture that log schemes in this class admit log crepant log resolutions. We provide some examples as evidence and relate the conjecture to the conjecture made joint work with Filip&Petracci, the Gross-Siebert program and the construction of Fano 3-folds.

5. Fano moduli for curves and quivers

Prof. Pieter Belmans

4/2/25, 11:00 AM

Moduli spaces of vector bundles on a curve are a classical and well-studied class of Fano varieties, with many interesting properties. Moduli spaces of quiver representations of an acyclic quiver are likewise (almost) Fano, with many interesting properties. There exists a rich dictionary between the two types of moduli spaces, explaining how phenomena for moduli of bundles have an analogue for...

3. Tom & Jerry triples unprojection format

Dr Vasiliki Petrotou

4/2/25, 1:00 PM

Unprojection is a theory introduced by Miles Reid which constructs more complicated Gorenstein rings starting from simpler data. This theory has found many applications in algebraic geometry and also in algebraic combinatorics. Tom and Jerry are two formats of unprojection defined and named by Miles Reid which lead to the construction of codimension 4 Gorenstein rings starting from codimension...

11. Categorical Torelli theorems for weighted hypersurfaces and the Veronese double cone

Prof. Jørgen Rennemo

4/2/25, 2:15 PM

The derived category of a Fano variety will often have a semiorthogonal decomposition consisting of a sequence of exceptional line bundles and a remaining subcategory, which we will call the Kuznetsov category. The categorical Torelli problem asks whether knowing this category up to exact equivalence is enough to determine the variety up to isomorphism. We will explain how a technique based on...

1. Fano 3-Fold weighted Hypersurfaces

Prof. Jihun Park

4/3/25, 8:30 AM

In this talk, we will explore the 130 families of Fano 3-fold weighted hypersurfaces, with a particular focus on their non-rationality and K-stability. This is an ongoing collaboration with T. Okada.

12. K-stability of Fano weighted hypersurfaces

Prof. Taro Sano

4/3/25, 9:45 AM

K-stability (or existence of Kähler-Einstein metrics) of
explicit Fano varieties has been studied for a long time.
Delta invariants (stability thresholds) detect the K-stability of Fano
varieties.
Moreover, Abban--Zhuang developed a powerful method to compute the
delta invariants by adjunctions.
In this talk, I will explain our recent results on the K-stability of
some Fano weighted...

9. New birational invariants for Fanos

Prof. Ludmil Katzarkov

4/3/25, 11:00 AM

In this talk we will introduce new birational invariants
inspired by HMS and CFT.
Many examples of nonrational and G nonrational
invariants will be introduced.

6. Cluster type variety

Prof. Joaquin Moraga

4/3/25, 1:00 PM

Toric varieties are ubiquitous objects in algebraic geometry. A toric variety can be described as a (partial) compactification of an algebraic torus such that the volume form of the torus has poles along every divisor added in the compactification. In this talk, we will introduce the concept of
cluster type varieties which are (partial) compactifications of algebraic tori such that the volume...

13. Birational mirrors to pairs of Laurent polynomials

Dr Hannah Tillmann-Morris

4/3/25, 2:15 PM

Under mirror symmetry, deformation classes of Fano varieties are associated to mutation classes of maximally mutable Laurent polynomials (MMLPs). We expect birational relationships between the general members of two deformation classes to be reflected, in the pair of mirror mutation classes, as combinatorial relationships between two MMLPs.

I will present an alternative construction of a...

2. Some log singular surfaces with unobstructed deformations

Dr Simon Felten

4/4/25, 8:30 AM

The logarithmic Bogomolov-Tian-Todorov theorem guarantees that infinitesimal deformations of a proper log Calabi--Yau space over a log point are unobstructed once certain cohomological conditions are met. We know that these conditions are satisfied for log smooth and more generally log toroidal spaces. In this talk, I report ongoing joint work with Matthias Zach where we check the...

7. Enumerative geometry of quantum periods

Dr Tim Gräfnitz

4/4/25, 9:45 AM

I talk about joint work with Helge Ruddat, Eric Zaslow and Benjamin Zhou interpreting the q-refined theta function of a log Calabi-Yau surface as a natural q-refinement of the open mirror map, defined by quantum periods of mirror curves for outer Aganagic-Vafa branes on the local Calabi-Yau threefold. The series coefficients are all-genus logarithmic two-point invariants, directly extending...

4. Relative mirror symmetry and some applications

Prof. Fenglong You

4/4/25, 11:00 AM

We consider mirror symmetry for a log Calabi--Yau pair (X,D), where X is a Fano variety and D is an anticanonical divisor of X. The mirror of the pair (X,D) is a Landau--Ginzburg model (X^\vee, W), where W is a function called the superpotential. Following the mirror constructions in the Gross--Sibert program, W can be described in terms of Gromov--Witten invariants of (X,D). I will explain a...

10. LSD Fanos

Prof. Michel van Garrel

4/4/25, 1:00 PM

Condition LSD (log smooth degeneration) states that the pair (Y,D) of Y=Fano and D=smooth anticanonical divisor admits a normal crossings degeneration to a union of blow ups of toric varieties.

Condition HDTV states that Y may be constructed via the HDTV mirror construction, a special case of intrinsic mirror symmetry.

The expectation is that LSD <=> HDTV. Moreover, they imply the...

14. Lefschetz hyperplane theorem for weighted projective spaces and cohomological invariants of Fano hypersurfaces

Mrs Anna-Maria Raukh

4/4/25, 2:15 PM

Given a generic hypersurface of a fixed degree in a n-dimensional weighted projective space, we describe the cohomology groups H^k for k<n and establish an explicit formula for the pullback map. Our results extend classical Lefschetz hyperplane theorem to weighted projective spaces and cohomology with integer coefficients. These results can be applied to compute cohomological invariants of...

16. Laurent polynomials and deformations of non-isolated Gorenstein toric singularities

Prof. Matej Filip

4/4/25, 3:30 PM

We establish a correspondence between one-parameter deformations of an affine Gorenstein toric variety X, defined by a polytope P, and mutations of a Laurent polynomial f, whose Newton polytope is equal to P. If the Newton polytope P of f is two dimensional and there exists a set of mutations of f that mutate P to a smooth polygon, then, we show that the Gorenstein toric variety, defined by P,...