Yonghwa Cho, Nodal Surfaces and Cubic Discriminants

     Speaker

Yonghwa Cho
IBS CCG

(This is a part of Seminars on Algebraic Surfaces and Related Topics.)

In this talk, I will explain how to associate a nodal surface in P3 with a cubic hypersurface, generalizing the method by Togliatti who constructed quintics with 31 nodes via a discriminant of a nodal cubic 4-folds. For low degrees(≤5), these constructions help to understand the classification problem of nodal surfaces, especially when the surface has the maximal number of nodes. For higher degrees the things get more complicated. I will explain our recent result on sextics proving that every nodal sextics with maximal number of nodes admit Togliatti type descriptions. This talk is based on joint works with Fabrizio Catanese, Stephen Coughlan, Davide Frapporti, Michael Kiermaier, and Sascha Kurz.

Seminars on Algebraic Surfaces and Related Topics

     Schedule

Feb. 27

      1. N-resolutions
        Giancarlo Urzua (UC Chille)
        13:30-14:20


      2. Smooth Projective Surfaces with Pseudo-effective Tangent Bundles
        Guolei Zhong (IBS-CCG)
        14:40-15:30


      3. Nodal Surfaces and Cubic Discriminants
        Yonghwa Cho (IBS-CCG)
        15:50-16:40


      4. Lagrangian Fibration Structure on the Cotangent Bundle of a Del Pezzo Surface of Degree 4
        Hosung Kim (IBS-CCG)
        17:00-17:50


      5. Dinner
        18:20-20:00

Feb. 28

      1. Deformations of Sandwiched Surface Singularities and the Minimal Model Program
        Dongsoo Shin (Chungnam National U.)
        10:00-10:50


      2. Mori Dream Surfaces of General Type with pg=0
        JongHae Keum (KIAS)
        11:10-12:00


      3. Lunch
        12:00-13:00

Korea-Japan Conference in Algebraic Geometry

Speakers

Yonghwa Cho (IBS-CCG)
Junho Choe (KIAS)
Yoshinori Gongyo (Tokyo U.)
Kenta Hashizume (Kyoto U.)
Sukmoon Huh (Sungkyunkwan U.)
WonTae Hwang (Jeonbuk National U.)
Seung-Jo Jung (Jeonbuk National U.)
Yeongrak Kim (Pusan National U.)
Tasuki Kinjo (IPMU, Tokyo)
Tatsuki Kuwagaki (Kyoto U.)
Shin-ichi Matsumura (Tohoku U.)
Yosuke Matsuzawa (Osaka Metropolitan U.)
Jinhyung Park (KAIST)
Kenta Sato (Kyushu U.)
Joonyeong Won (Ehwa Womans U.)
Shou Yoshikawa (RIKEN iTHEMS)

Abstracts

PDF File

Schedule

Day 1: February 13 (Monday)

~10:00 Registration
10:00~11:00 Jinhyung Park
Syzygies of tangent developable surfaces and K3 carpets via secant varieties
Jun-Muk Hwang
(Chair)
11:00~11:30 Coffee Break
11:30~12:30 Shin-ichi Matsumura
The nonvanishing problem for varieties with nef anticanonical bundle
12:30~14:30 Lunch
15:00~16:00 Seung-Jo Jung
On Milnor numbers and Tjurina numbers of hypersurface singularities
Yujiro Kawamata
(Chair)
16:00~16:20 Coffee Break
16:20-17:20 Yosuke Matsuzawa
Zariski dense orbit conjecture and arithmetic degrees of cohomologically hyperbolic maps
18:00~20:00 Speakers Dinner

 

Day 2: February 14 (Tuesday)

10:00~11:00 Yoshinori Gongyo
Generalized complexities and the Mukai type conjecture
Yongnam Lee
(Chair)
11:00~11:30 Coffee Break
11:30~12:30 Shou Yoshikawa
Quasi-F-splitting
12:30~14:30 Lunch
15:00~16:00 Sukmoon Huh
Torelli problem on logarithmic sheaves
Sijong Kwak
(Chair)
16:00~16:20 Coffee Break
16:20-17:20 Kenta Sato
General hyperplane section of log canonical threefolds in positive characteristic

 

Day 3: February 15 (Wednesday)

10:00~11:00 WonTae Hwang
Jordan constants of groups in connection with abelian varieties in positive characteristic
Dongseon Hwang
(Chair)
11:00~11:30 Coffee Break
11:30~12:30 Tasuki Kinjo
Euler characteristic for stacks
12:30~18:00 Excursion

 

Day 4: February 16 (Thursday)

10:00~11:00 Junho Choe
Various parallels between projective varieties and secant varieties
Jaehyun Hong
(Chair)
11:00~11:30 Coffee Break
11:30~12:30 Tatsuki Kuwagaki
Some examples of Hodge-Fukaya theory
12:30~14:30 Lunch
15:00~16:00 Joonyeong Won
Twisted Kaehler-Einstein metric on del Pezzo surfaces
JongHae Keum
(Chair)
16:00~16:20 Coffee Break
16:20-17:20 Kenta Hashizume
On effective base point freeness for klt pairs
17:30~19:00 Banquet

 

Day 5: February 17 (Friday)

10:00~11:00 Yeongrak Kim
Ulrich bundles on cubic fourfolds
Keiji Oguiso
(Chair)
11:00~11:30 Coffee Break
11:30~12:30 Yonghwa Cho
Nodal (hyper-)surfaces

Organizers

Osamu Fujino (Kyoto U.)
DongSeon Hwang (IBS-CCG)
Jun-Muk Hwang (IBS-CCG)
Yongnam Lee (IBS-CCG)
Keiji Oguiso (U. Tokyo)
Shunsuke Takagi (U. Tokyo)

Registration

Please submit Google form by January 31.

More Information

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Yonghwa Cho, Nodal Sextics and Even Sets of Nodes

     Speaker

Yonghwa Cho
IBS CCG
It is a classical question to ask how many nodes may a surface contain. For sextics, the maximum number of nodes is 65, and is attained by Barth’s example. We ask further: are all sextics with 65 nodes like Barth’s example? To find an answer, we study even sets of nodes on sextic surfaces, and prove that all sextics with 65 nodes share the same structure of even sets. This establishes a resemblance between Barth’s sextic and other sextics with 65 nodes. This talk is based on a joint work with Fabrizio Catanese, Michael Kiermaier, and Sascha Kurz.

Yonghwa Cho, Cohomology of Divisors on Burniat Surfaces

     Speaker

A (primary) Burniat surface is a complex surface of general type that can be obtained as a bidouble cover of del Pezzo surface with K2 = 6. The Picard group is an abelian group of rank 4 with torsion part isomorphic to (Z/2)6. Alexeev studied the divisors on Burniat surfaces, and observed that the irreducible components of ramification divisors span the semigroup of effective divisors. Based on Alexeev’s result, I will describe the method for computing cohomology of arbitrary divisors on Burniat surfaces. If time permits, (non-)existence question about Ulrich bundles will be discussed as an application.

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