Mini-Workshop on Algebraic Surfaces

Invited Speakers

• Yifan Chen _ Beihang University
• DongSeon Hwang _ Ajou University
• In-Kyun Kim _ Sungkyunkwan University
• YongJoo Shin _ Korea Institute for Advanced Study
• Joonyeong Won _ Korea Institute for Advanced Study

Program

• 10:00--11:00 Yifan Chen

The 4-nodal cubic surface and certain surfaces of general type with geometric genus zero

After briefly describing the geometry of the 4-nodal cubic surface, I will introduce the Keum-Naie-Mendes Lopes-Pardini surfaces. Then I will talk about the bicanonical map, the deformation and moduli of these surfaces.

• 11:20--12:20 DongSeon Hwang

Introduction to Manin’s conjecture

Manin’s conjecture predicts the asymptotic distribution on the rational points on Fano varieties. In this talk, I will try to explain the historical development of the conjecture and explain the connection between geometry and arithmetic in the case of a log del Pezzo surface with A_4 and K_5 singularities. This is based on joint work in progress with Ulrich Derenthal.

• Lunch

• 14:00--15:00 In-Kyun Kim

K-stability of log del Pezzo surfaces with small alpha-invariants

In this talk, we estimate beta-invariants and delta-invariant of some singular log del Pezzo surfaces with quotient singularities. As a result we prove their K-stability and the existence of K\”ahler-Einstein metrics.

• 15:20--16:20 YongJoo Shin

Fibrations of hyperelliptic curves of genus $3$ on minimal surfaces of general type with $p_g=0$

In this talk we consider results and examples of fibrations of hyperelliptic curves of genus $3$ with double fibers on minimal surfaces of general type with $p_g=0$. As its application we construct smooth minimal $3$-folds of general type canonically fibred by surfaces of geometric genus $37$. It gives an answer of a question of Chen and Cui.

• 16:40--17:40 Joonyeong Won

Sasaki-Einstein metrics on simply connected rational homology 5-spheres

By developing the method introduced by Kobayashi in 1960’s, Boyer, Galicki and Kollár found many examples of simply connected Sasaki-Einstein 5-manifolds. For such examples they verified existence of orbifold Kaehler-Einstein metrics on various log del Pezzo surfaces via links. By the recent development of method to verify existence of orbifold Kaehler-Einstein metrics, we complete the classification of simply connected rational homology 5-spheres that admits Sasaki-Einstein metrics. This is a joint work with Jihun Park.

• Dinner 18:00--

Organizing Committee

• JongHae Keum _ Korea Institute for Advanced Study
• Dongsoo Shin _ Chungnam National University
• YongJoo Shin _ Korea Institute for Advanced Study

Sponsored by

• Korea Institute for Advanced Study
• Korea National Research Foundation

Contact

• Dongsoo Shin: dsshin@cnu.ac.kr