신동수 Dongsoo Shin

• 이메일: dsshin@cnu.ac.kr

• 홈페이지: https://sites.google.com/site/eopqed

관심분야: 대수기하학 Field of research: Algebraic Geometry

• 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

연구논문 Research Papers

1. 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 

2. 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)

3. 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

4. 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

5. 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 

6. 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)

7. 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

8. Rational homology balls in $2$-handlebodies
   Bulletin of the Korean Mathematical Society 54 (2017), no. 6, 1927--1933 (with Heesang Park), arXiv:1803.05781

9. 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)

10. 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

11. Conics on a general hypersurface in $\mathbb{P}^n$
    Bulletin of the Korean Mathematical Society 50 (2013), no. 6, 2071--2077

12. 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

13. 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

14. 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)

15. 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 

16. 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

17. 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

18. 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

19. Base-point-free pencils on triple covers of smooth curves
    International Journal Mathematics 19 (2008), no. 6, 1--27, arXiv:0806.1849

20. Rational curves on general hypersurfaces of degree $7$ in $\mathbf{P}^5$
    Osaka Journal Mathematics 44 (2007), 1--10

21. 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)

프리프린트 Preprints

1. Anti-MMP approach to deformations of sandwiched surface singularities
   (with Heesang Park)

2. Rational homology balls in Milnor fibers of cyclic quotient surface singularities
   (with Heesang Park)

3. Deformations of weighted homogeneous surface singularities admitting rational homology disk smoothings
   (with Jaekwan Jeon and Heesang Park)

4. Deformations of weighted homogeneous surface singularities with big central node, arXiv:2305.14738  (with Jaekwan Jeon)

5. Deformations of sandwiched surface singularities and the minimal model program, arXiv:2205.11165 (with Heesang Park)

6. Normal complex surface singularities with rational homology disk smoothings, arXiv:1311.1929 (with Heesang Park, András Stipsicz)

(주관한) 대수곡면론 학회 Workshops on Algebraic Surfaces (organized by me+others)

• 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

연구비 Research Grant

• 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

기초연구실 Basic Research Laboratory

《복소곡면의 퇴화의 대수기하학적 그리고 사교위상수학적 측면》

• 기간: 2021.06.01--2024.02.29 (33개월)

• 연구비: 한국연구재단 지원 / 총 13억 7천 500만원

• 홈페이지