Publication
Publication
1. Compactified moduli spaces of rational curves in a projective variety. Thesis, 2011.
2. Hilbert scheme of rational cubic curves via stable maps (with Young-Hoon Kiem), Amer. J. Math. 133 (2011), no. 3, 797-834.
3. Compactified moduli spaces of rational curves in projective homogeneous varieties (with Jae-Hyun Hong and Young-Hoon Kiem), J. Math. Soc. Japan. 64 (2012), no. 4, 1211-1248.
4. The geometry of the moduli space of one-dimensional sheaves (with Jinwon Choi), Science China-Mathematics, Sep. (2014), DOI: 10.1007/s11425-014-4889-9.
5. Cohomology bounds for sheaves of dimension one (with Jinwon Choi), International Journal of Mathematics, Nov. (2014), DOI: 10.1142/S0129167X14501031.
6. Virtual Poincare polynomial of the space of stable pairs supported on quintic curves, Journal of Geometry and Physics, 94, Aug. (2015), 209–217.
7. Twisted cubic curves in the Segre variety (with Wanseok Lee), Comptes Rendus Mathematique, 353 (2015), no.12, 1123–1127.
8. Moduli of sheaves, Fourier-Mukai transform, and partial desingularization (with Han-Bom Moon), Math. Z. 283 (2016), no.1, 275-299.
9. Moduli spaces of α-stable pairs and wall-crossing on P^2 (with Jinwon Choi), J. Math. Soc. Japan. Vol. 68 (2016), No. 2, 685-789.
10. Moduli of sheaves supported on quartic space curves (with Jinwon Choi and Mario Maican), Michigan Math. J. Vol. 65 (2016), no. 3, 637-671.
11. On the space of smooth rational curves of maximal regularity (with Wanseok Lee and Euisung Park), Manuscripta Mathematica. Nov. (2016), Vol.151, no. 3, 505–518.
12. Mori's program for the moduli space of conics in Grassmannian (with Han-Bom Moon), Taiwanese Journal of Mathematics, Vol. 21, No. 3, 621–652, June 2017
13. Chow ring of the moduli space of stable sheaves supported on quartic curves (with Han-Bom Moon), Quarterly Journal of Mathematics, Vol.68, No. 3, 851–887, Sep. 2017
14. Stable maps of genus zero in the space of stable vector bundles on a curve (with SangHyeon Lee), International Journal of Mathematics, Vol. 28 (11), Oct. 2017, 1-18.
15. Birational geometry of the moduli space of pure sheaves on quadric surface (with Han-Bom Moon), Comptes rendus - Mathematics, Vol. 355 (10), Oct. 2017, 1082-1088.
16. Geometry of moduli spaces of rational curves in linear sections of Grassmannian $Gr(2,5)$ (with Jae-Hyun Hong and SangHyeon Lee), Journal of Pure and Applied Algebra, Vol. 222 (04), Apr. 2018, 868-888.
17. Geometry of moduli space of sheaves on del Pezzo surfaces via Maruyama transform (with Jinwon Choi), Journal Communications in Algebra, 47(2), 2019, 907-916.
18. Compactifications of conic spaces in del Pezzo $3$-fold (with Sang-Bum Yoo), Comptes rendus - Mathematics, 357 (9), Sep. 2019, 729-736.
19. Curves in Segre threefolds (with Edoardo Ballico and Sukmoon Huh), Forum Mathematicum, 32 (1), Jan. 2020, 63–78.
20. Intersection cohomology of pure sheaf spaces using Kirwan's desingularization (with Youngho Yoon), Journal of Geometry and Physics, Vol. 160, Feb. 2021, 103992.
21. Sheaf theoretic compactifications of the space of rational quartic plane curves, Taiwanese Journal of Mathematics, Vol. 25, No. 3, pp. 463–476, June 2021.
22. Minimal rational curves on the moduli spaces of symplectic and orthogonal bundles (with Insong Choe and SangHyeon Lee), Journal of the London Mathematical Society, Vol 105, No.1, Jan. pp. 543-564, 2022.
23. Double lines in the quintic del Pezzo fourfold, Bulletin of the Korean Mathematical Society, Vol 60, No.2, Mar., 485-494, 2023.
24. Desingularization of Kontsevich’s compactification of twisted cubics in $𝑉_5$, Manuscripta Math. 171, May, 347–367, 2023.
25. Conics in quintic del Pezzo varieties (with SangHyeon Lee), Journal of the Korean Mathematical Society, 61(2), 357-375, Mar., 2024
26. Correspondence of Donaldson-Thomas and Gopakumar-Vafa invariants on local Calabi-Yau 4-folds over $V_5$ and $V_22$ (with SangHyeon Lee and Joonyeong Won), Journal of Geometry and Physics, Vol. 197, Mar. 2024, 105082.
27. An $\text{SL}(3,\mathbb{C})$-equivariant smooth compactification of moduli space of rational quartic plane curves (with Jeong-Seop Kim), Journal of Algebra, Volume 645, May, 94-115, 2024.
Submitted Papers and preprints
28. Rational curves in a quadric threefold via an $\text{SL}(2,\mathbb{C})$-representation (with Sukmoon Huh and Sang-Bum Yoo), submitted, arXiv: 2301.11539
29. Survey on rational quartic curves in Fano $3$-folds $X$ with $\rho(X)=b_2(X)=1$ , preprint
30. Birational relation of Hilbert scheme of rational curves in $\mathbb{P}^3$ and $Q_3$, preprint
31. Derived wall-crossings of the moduli space of stable sheaves supported on rational quartic space curves, preprint
32. Global geometry of the moduli space of stable pairs on Fano threefolds (with Sang-Bum Yoo), preprint
Book
1. 임용수학 완전정복 미분기하학 (김영록, 한종민 공저, 경문사, 2018년 4월)
2. 플립러닝을 위한 대수학: 군론편 (준비중), 최성락, 원준영, 박진형, 홍규식, 김인균 공저, 강의영상(YouTube))
3. 플립러닝을 위한 대수학: 환, 체 그리고 갈루아 이론편, 최성락, 원준영, 박진형, 홍규식, 박유진, 송은정 공저