In 1986, Green-Lazarsfeld raised the gonality conjecture asserting that the gonality gon(C) of a smooth projective curve C of genus g can be read off from weight-one syzygies of a sufficiently positive line bundle L, and also proposed possible least degree of L, that is 2g+gon(C)-1. In 2015, Ein-Lazarsfeld proved the conjecture when deg(L) is sufficiently large, but the effective part of the conjecture remained widely open and was reformulated explicitly by Farkas-Kemeny a few years ago. We show an effective vanishing theorem for weight-one syzygies, which implies that the gonality conjecture holds if deg(L) is at least 2g+gon(C) or equal to 2g+gon(C)-1 and C is not a plane curve. As Castryck observed that the gonality conjecture may not hold for a plane curve when deg(L)=2g+gon(C)-1, this result is the best possible and thus gives a complete answer to the gonality conjecture. This is joint work with Wenbo Niu.
Workshop on Classical Algebraic Geometry
Speakers
Alberto Calabri (University of Ferrara)
Cinzia Casagrande (University of Torino)
Flaminio Flamini (University of Rome Tor Vergata)
Paola Frediani (University of Pavia)
Kangjin Han (DGIST)
Zhi Jiang (SCMS, Fudan University)
Akihiro Kanemitsu (Saitama University)
Grzegorz Kapustka (Jagiellonian University)
Michał Kapustka (IM PAN)
Seonja Kim (Chungwoon University)
Hirokazu Nasu (Tokai University)
Wenbo Niu (University of Arkansas)
Jinhyung Park (KAIST)
Xavier Roulleau (University of Angers)
Francesco Russo (University of Catania)
Eduardo Luis Solá Conde (University of Trento)
Abstracts
Schedule
December 12 (Tuesday)
| 09:30~10:00 | Registration |
| 10:00~11:00 | Cinzia Casagrande |
| 11:00~11:30 | Coffee Break |
| 11:30~12:30 | Jinhyung Park |
| 12:30~14:30 | Lunch |
| 14:30~15:30 | Seonja Kim |
| 15:30~16:00 | Coffee Break |
| 16:00~17:00 | Eduardo Luis Solá Conde |
| 18:00~20:00 | Dinner for Speakers |
December 13 (Wednesday)
| 10:00~11:00 | Flaminio Flamini |
| 11:00~11:30 | Coffee Break |
| 11:30~12:30 | Hirokazu Nasu |
| 12:30~14:30 | Lunch |
| 14:30~15:30 | Zhi Jiang |
| 15:30~16:00 | Coffee Break |
| 16:00~17:00 | Akihiro Kanemitsu |
December 14 (Thursday)
| 10:00~11:00 | Michał Kapustka |
| 11:00~11:30 | Coffee Break |
| 11:30~12:30 | Grzegorz Kapustka |
| 12:30~14:30 | Lunch |
| 14:30~15:30 | Alberto Calabri |
| 15:30~16:00 | Coffee Break |
| 16:00~17:00 | Francesco Russo |
| 17:30~20:00 | Banquet |
December 15 (Friday)
| 10:00~11:00 | Xavier Roulleau |
| 11:00~11:30 | Coffee Break |
| 11:30~12:30 | Wenbo Niu |
| 12:30~14:00 | Lunch |
| 14:00~15:00 | Kangjin Han |
| 15:00~15:30 | Coffee Break |
| 15:30~16:30 | Paola Frediani |
Organizers
DongSeon Hwang (IBS-CCG)
Jun-Muk Hwang (IBS-CCG)
Yongnam Lee (IBS-CCG/KAIST)
Venue
IBS Science Culture Center
Registration
Please submit Google form by November 10th.
Main Hotel
Lotte City Hotel Daejeon (4-30 Doryong-dong, Yuseong-gu, Daejeon)
More Information
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
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
Jinhyung Park, Comparing Numerical Iitaka Dimensions
There are several definitions of the “numerical” Iitaka dimensions of a pseudoeffective divisor, which are numerical analogues to the Iitaka dimension. Recently, Lesieutre proved that notions of numerical Iitaka dimensions do not coincide. In this talk, we prove that many of numerical Iitaka dimensions are equal to the notion introduced by Boucksom-Demailly-Paun-Peternell and that some other invariants introduced by Nakayama and Lehmann can be arbitrarily larger than this notion. We also show some properties of abundant divisors. This is joint work with Sung Rak Choi.