복소곡면 특이점의 변형
Deformations of complex surface singularities
복소곡면 특이점의 기하와 위상
Geometry and Topology of complex surface singularities
기하종수가 작은 일반형 복소곡면과 모듈라이 공간
Complex surfaces of general type with small geometric genus and their moduli spaces
$\mathbb{Q}$-Gorensteiness of rational homology disk smoothings of weighted homogeneous surface singularities
Journal of the Korean Mathematical Society 63 (2026), No. 3, pp. 509--539 (with Jaekwan Jeon, Heesang Park)
The Kollár conjecture for $W_{p,q,r}$
Communications of the Korean Mathematical Society 41 (2026), No. 2, pp. 351--372 (with Heesang Park)
Rational homology balls in Milnor fibers of cyclic quotient surface singularities
Bulletin of the Korean Mathematical Society 61 (2024) no. 6, pp. 1459--1466 (with Heesang Park)
Symplectic rational blowdown on rational 4-manifolds
Proceedings of the American Mathematical Society 152 (2024) no. 3, 1309--1318 (with Heesang Park), arXiv:2111.07501
Lens spaces admitting minimal symplectic fillings with the second Betti number one
Bulletin of the Korean Mathematical Society 60 (2023) no. 1, 113--122 (with Heesang Park)
Simple embeddings of rational homology balls and antiflips
Algebraic & Geometric Topology 21 (2021) no. 4, 1857--1880 (with Heesang Park, Giancarlo Urzúa), arXiv:1904.04927
Symplectic fillings of quotient surface singularities and minimal model program,
Journal of the Korean Mathematical Society 58 (2021) no. 2, 419--437 (with Hakho Choi, Heesang Park), arXiv:1811.07373
Invariants of deformations of quotient surface singularities
Journal of the Korean Mathematical Society 56 (2019), no. 5, 1173--1246 (with Byoungcheon Han, Jaekwan Jeon), arXiv:1803.00142
Complex surfaces of general type with $K^2=3,4$ and $p_g=q=0$,
Comptes Rendus Mathématique 357 (2019), no. 3, 291--295 (with Heesang Park, Yoonjeong Yang)
Milnor fibers and symplectic fillings of quotient surface singularities
Advances in Mathematics 329 (2018), 1156--1230 (with Heesang Park, Jongil Park, Giancarlo Urzúa), arXiv:1507.06756
Rational homology balls in $2$-handlebodies
Bulletin of the Korean Mathematical Society 54 (2017), no. 6, 1927--1933 (with Heesang Park), arXiv:1803.05781
Simply connected complex surfaces of general type with $p_g=0$ and $K^2=1,2$
Communications of the Korean Mathematical Society 32 (2017), no. 3, 479--494 (with Heesang Park, Jongil Park, Ki-Heon Yun)
Smoothly embedded rational homology balls
Journal of the Korean Mathematical Society 53 (2016), no. 6, 1293--1308 (with Heesang Park, Jongil Park), arXiv:1508.03724
Conics on a general hypersurface in $\mathbb{P}^n$
Bulletin of the Korean Mathematical Society 50 (2013), no. 6, 2071--2077
A complex surface of general type with $p_g=0$, $K^2=2$ and $H_1=\mathbb{Z}/4\mathbb{Z}$
Transactions of the American Mathematical Society 365 (2013), no. 11, 5713--5736 (with Heesang Park, Jongil Park), arXiv:1012.5871
A simply connected numerical Campedelli surface with an involution
Mathematische Annalen 357 (2013), no. 1, 31--49 (with Heesang Park, Giancarlo Urzúa), arXiv:1108.0797
Surfaces of general type with $p_g=1$ and $q=0$
Journal of the Korean Mathematical Society 50 (2013), no. 3, 493--507 (with Heesang Park, Jongil Park), arXiv:0906.5195 (+ arXiv:0910.3506)
A complex surface of general type with $p_g=0$, $K^2=3$ and $H_1=\mathbb{Z}/2\mathbb{Z}$
Bulletin of the Korean Mathematical Society 47 (2010), no. 6, 1269--1274 (with Heesang Park, Jongil Park), arXiv:0803.1322
The minimal degree of plane models of double covers of smooth curves
Journal of Pure and Applied Algebra 214 (2010), no. 7, 1001--1010, arXiv:0809.853
A simply connected surface of general type with $p_g=0$ and $K^2=4$
Geometry & Topology 13 (2009), no. 3, 1483--1494 (with Heesang Park, Jongil Park), arXiv:0803.3667
A simply connected surface of general type with $p_g=0$ and $K^2=3$
Geometry & Topology 13 (2009), no. 2, 743--767 (with Heesang Park, Jongil Park), arXiv:0708.0273
Erratum: Geometry & Topology 15 (2011), no. 1, 499--500
Base-point-free pencils on triple covers of smooth curves
International Journal Mathematics 19 (2008), no. 6, 1--27, arXiv:0806.1849
Rational curves on general hypersurfaces of degree $7$ in $\mathbf{P}^5$
Osaka Journal Mathematics 44 (2007), 1--10
Pencils on coverings of a given curve whose degree is larger than the Castelnuovo-Severi lower bound
Bull. Inst. Math. Acad. Sin. (N.S.) 2 (2007), no. 1, 103--107 (with Edoardo Ballico, Changho Keem)
The classification of taut surface singularities via representations from logarithmic vector fields
arXiv:2610.25654 preprint (with Heesang Park)
Weighted homogeneous surface singularities admitting rational homology disk smoothings
arXiv:2610.24936 (with Heesang Park)
Nonlinear neighborhoods of smooth curves and arbitrarily negative Wahl defects
arXiv:2610.21093 (with Heesang Park)
Positivity of Wahl defects and specialization of reflexive powers of the canonical sheaf
arXiv:2610.21092 (with Heesang Park)
Normal complex surface singularities with rational homology disk smoothings
arXiv:2610.20991 (Márton Beke, Heesang Park, András Stipsicz)
Deformations of weighted homogeneous surface singularities with big central node,
arXiv:2305.14738 (with Jaekwan Jeon, Heesang Park)
Stable cohomology modules and universal nonlinear blowdowns
preprint (with Heesang Park)
We characterize, via Fitting strata of a stable cohomology module, the base changes for which the Remmert contraction of a marked negative-definite SNC family is flat, fiberwise normal, and compatible with arbitrary analytic base change.
Intrinsic persistence of rational surface resolutions
preprint (with Heesang Park)
We construct intrinsically from an unresolved deformation of a rational surface singularity the locus where its minimal good resolution persists, prove Lipman–Douady representability and arrow rigidity, and identify this locus with a target-side valuative–Rees equisingularity locus.
Integral vanishing lattices and marked $\mathbb Q$-Gorenstein degenerations of rational surfaces
preprint (with Jaekwan Jeon, Heesang Park, Yoonjeong Yang)
We prove integral vanishing-lattice constraints for $\mathbb Q$-Gorenstein degenerations of rational surfaces and use them, together with marked local deformation data and explicit toric Cox pencils, to classify the Picard-number-one cases with one non-Wahl class-$T$ singularity by four Markov-type equations.
Tjurina numbers of the Okuma surface singularity family
submitted (with Heesang Park)
We compute the Tjurina numbers of the Okuma surface family of isolated Cohen--Macaulay codimension-two surface singularities.
Numerical Godeaux surfaces with $H_1=\mathbb{Z}/4\mathbb{Z}$
submitted (with Yoonjeong Yang)
We construct minimal complex surfaces of general type with $K^2=1$, $p_g=q=0$, and $H_1=\mathbb{Z}/4\mathbb{Z}$ as double covers of Enriques surfaces.
2025.10.31: Algebraic Surfaces and Their Singularities
2024.06.27--06.28: Singularities in Algebraic Geometry and Symplectic Topology
2024.01.22--01.27: Topology of 4-manifolds and related topics
2023.02.21: One-day Workshop on Derived Category
2023.02.01--02.03: Geometry and Topology of Deformations of Complex Surface Singularities
2019.12.06: Mini Workshop on Algebraic Surfaces 2019
2019.06.24--06.28: Algebraic and Symplectic Aspects in Degenerations of Complex Surfaces
2017.07.17: Mini Workshop on Algebraic Surfaces 2017
2016.01.25--01.27: Winter School on Algebraic Surfaces 2016
2015.01.28--01.30: Winter School on Algebraic Surfaces 2015
2023-03-01 ~ 2028-02-29: 샌드위치된 곡면 특이점의 새로운 변형 이론 / 한국연구재단, 중견연구
2021-06-01 ~ 2024-02-29: 복소곡면의 퇴화의 대수기하학적 그리고 사교위상수학적 측면 / 한국연구재단, 기초연구실
2018-06-01 ~ 2023-05-31: 유리곡면특이점의 밀너가닥과 사교채움 / 한국연구재단, 기본연구
2015-11-01 ~ 2018-10-31: 복소곡면 특이점의 변형공간과 불변량 / 한국연구재단, 기본연구
2014-12-01 ~ 2019-11-30: 일반형 복소곡면의 모듈라이 공간의 새로운 옹골화 이론 연구 / 삼성미래기술육성재단
2013-06-01 ~ 2016-05-31: 기하종수가 작은 일반형 복소곡면과 모듈라이 공간 / 한국연구재단, 기본연구
2010-05-01 ~ 2013-04-30: 작은 기하종수를 갖는 일반형 복소곡면 / 한국연구재단, 신진연구
기간: 2021.06.01--2024.02.29 (33개월)
연구비: 한국연구재단 지원 / 총 13억 7천 500만원