Publication List

Young-Hoon Kiem

Research Articles

1. Cohomology of quotients and moduli spaces of vector bundles: Doctoral Thesis, Yale University, May 2000.

2. On the redundancy of the Mumford relations: Journal of Algebraic Geometry 9 (2000), 395-402.

3. The equivariant cohomology ring of the moduli space of vector bundles over a Riemann surface: Proceedings of the Aarhus conference on Geometry and Topology, Contemporary Mathematics 258, AMS.

4. Intersection cohomology of quotients of nonsingular varieties: Inventiones Mathematicae 155, pp163-202 (2004).

5. (with Lisa Jeffrey, Frances Kirwan, Jon Woolf) Cohomology pairings on singular quotients in geometric invariant theory: Transformation Groups, Vol 8, No 3, pp 217-259 (2003).

6. The stringy E-function of the moduli spaces of rank 2 bundles over a Riemann surface of genus 3: Trans. Amer. Math. Soc. 355, no 5, pp1843-1856 (2003).

7. Chern classes of moduli of vector bundles over curves: Algebraic Geometry and Related Topics, Proceedings of the Korea-Japan Joint Workshop in Mathematics 2002, Yamaguchi University (2003).

8. (with Jun Li) Desingularizations of the moduli space of rank 2 bundles over a curve: Math Annalen 330, pp 491-518 (2004).

9. On the existence of a symplectic desingularization of some moduli spaces of sheaves on a K3 surface: Compositio Mathematica 141, issue 4, pp902-906, July 2005.

10. (with Jon Woolf) Intersection cohomology of symplectic quotients by circle actions: Jour. Lond. Math. Soc. 71, April 2005.

11. (with Insong Choe and Jaeyoo Choy) Cohomology of the moduli space of Hecke cycles: Topology, volume 44, issue 3, May 2005, pp585-608.

12. (with Jun Li) Vanishing of the top Chern classes of the moduli of vector bundles: Journal of Differential Geometry, Vol. 76 No. 1, pp45-115, May 2007.

13. (with Jaeyoo Choy) Nonexistence of crepant resolution of moduli space of sheaves on a K3 surface: Journal of Korean Mathematical Society, Vol. 44, pp35-54, January 2007.

14. Intersection cohomology of representation spaces of surface groups: International J. of Math., Vol 17. No 2, 169-182, February 2006.

15. (with Jaeyoo Choy) On the existence of a crepant resolution of some moduli spaces of sheaves on an abelian surface: Mathematische Zeitschrift252, 557-575, March 2006.

16. (with Jon Woolf) The Kirwan map for singular symplectic quotients: Jour. Lond. Math. Soc. 73, pp209-230, February 2006.

17. (with Lisa Jeffrey, Frances Kirwan, Jon Woolf) Intersection pairings on singular moduli spaces of bundles over a Riemann surface and their partial desingularizations: Transformation Groups, Vol. 11, No 3, pp439-494 , September 2006.

18. (with Sang-Bum Yoo) The stringy E-function of the moduli space of Higgs bundles with trivial determinant: Math. Nach. Vol.281, No.6 (2008), pp817-838.

19. Hecke correspondence, stable maps and the Kirwan desingularization: Duke Math. J., Vol. 136, No 3 (2007), pp585-618.

20. (with Jun Li) Gromov-Witten invariants of varieties with holomorphic 2-forms: Unpublished.

21. (with Han-Bom Moon) Moduli spaces of stable maps to projective space via GIT: International J. of Math., Vol. 21, No 5 (2010), pp639-664.

22. (with Lisa Jeffrey and Frances Kirwan) On the cohomology of hyperkahler quotients: Transformation Groups, Vol. 14, No 4, pp801-823, December 2009.

23. (with Kiryong Chung) Hilbert scheme of rational cubic curves via stable maps: American. J. Math., Vol. 133, No 3 (2011), 797~834.

24. (with Han-Bom Moon) Moduli spaces of weighted pointed stable rational curves via GIT: Osaka J. of Math., Vol. 48, No. 4 (2011), 1115~1140.

25. Birational geometry of moduli spaces of rational curves in projective varieties: Proceedings of the RIMS conference on Higher Dimensional Algebraic Geometry, Bessatu B24, RIMS, 67~79.

26. (with Jaehyun Hong and Kiryong Chung) Compactified moduli spaces of rational curves in projective homogeneous varieties: Journal of Math. Soc. of Japan, Vol. 64, No. 4 (2012), 1211-1248, October 2012.

27. Curve counting and birational geometry of compactified moduli spaces of curves: Proceedings of the Waseda symposium on algebraic geometry, November 2010.

28. (with Jinwon Choi) A new method toward the Landau-Ginzburg/Calabi-Yau correspondence via quasi-maps:  Math. Z. (2020) 294, 161~199 (Published online on Feb. 11, 2019, https://doi.org/10.1007/s00209-019-02249-1)

29. (with Jun Li) Low degree GW invariants of spin surfaces: Pure and Applied Math. Quarterly Vol. 7, No. 4 (2011), 1449~1476. (Special Issue: In memory of Eckart Viehweg.)

30. (with Jun Li) Low degree GW invariants of surfaces II: Science China Math. Vol. 54, No. 8 (2011), 1679~1706. (Special Issue: F. Catanese 60thBirthday.)

31. (with Seung-Hyeok Kye and Jungseob Lee) Existence of product vectors and their partial conjugates in a pair of spaces: Journal of Mathematical Physics Vol.52, Issue 12 (2011), 1~10.

32. (with Jun Li) A wall crossing formula of Donaldson-Thomas invariants without Chern-Simons functional: Asian J. Math. Vol. 17, No. 1, pp 63~94, March 2013.

33. (with Huailiang Chang) Poincare invariants are Seiberg-Witten invariants: Geometry and Topology, Vol. 17, 1149~1163, March 2013.

34. (with Jun Li) Localizing virtual cycles by cosections: Journal of Amer. Math. Soc. Vol. 26, No. 4, 1025~1050, October 2013.

35. (with Jun Li) Categorification of Donaldson-Thomas invariants via perverse sheaves: First half published in the Journal of Korean Mathematical Society, Vol. 55 No. 3 (2018), 623-669 with title "Critical virtual manifolds and perverse sheaves".

36. (with Seung-Hyeok Kye and Joohan Na) Product vectors in the ranges of multi-partite states with positive partial transposes and permanents of matrices: Communications in Mathematical Physics, Vol. 338, Issue 2, 621~639, September 2015.

37. (with Huailiang Chang and Jun Li) Torus localization and wall crossing formulas for cosection localized virtual cycles: Advances in Mathematics, Vol. 308, 964~986, 2017. 

38. (with In-Kyun Kim, Hwayoug Lee and Kyoung-Seog Lee) All complete intersection varieties are Fano visitors: Advances in Mathematics, Vol. 311, 649~661, 2017.

39. (with Kyoung-Seog Lee) Fano visitors, Fano dimension and Fano orbifolds : Birational geometry, Kahler-Einstein metrics and degenerations, 517-544, Springer Proc. Math. Stat. 409, Springer, 2023. 

40. Localizing virtual fundamental cycles for semi-perfect obstruction theories: International J. Math. Vol. 29, No. 4 (2018) 1850032 (30pages).

41. (with Jun Li) Localizing virtual structure sheaves by cosections:  International Mathematics Research Notices,  Vol. 2020, Issue 22, November 2020, Pages 8387–8417, https://doi.org/10.1093/imrn/rny235 

42. (with Jun Li and Michail Savvas) Generalized Donaldson-Thomas invariants via Kirwan blowups: To appear in the Journal of Differential Geometry.

43. (with Jun Li) Quantum singularity theory via cosection localization:  J. Reine Angew. Math. 766 (2020), 73–107. 

44. (with Jun Li and Huailiang Chang) Algebraic virtual cycles for quantum singularity theories: Comm. in Analysis and Geometry, Vol 29, No 8 (2021), 1749-1774.

45. (with Jaeseong Heo) On characterizing integral zeros of Krawtchouk polynomials by quantum entanglement: Linear Algebra and its Applications 567 (2019), 167-179.

46. (with Jinwon Choi and Seung-Hyeok Kye) Entangled edge states of corank one with positive partial transposes: Journal of Mathematical Physics 61, Issue 6 (June 2020), 062202 (2020); https://doi.org/10.1063/1.5122836. 

47. (with Hyeonjun Park) Virtual intersection theories: Advances in Mathematics 388, 107858, September 17 2021. 

48. (with Michail Savvas) K-theoretic generalized Donaldson-Thomas invariants: International Mathematics Research Notices, Vol. 2022, Issue 3, February 2022, Pages 2123–2158.

49. (with Michail Savvas) Localizing virtual structure sheaves for almost perfect obstruction theories: Forum of Mathematics Sigma 8 (2020.12.07), Paper No. e61, 1-36. 

50. (with Hyeonjun Park) Localizing virtual cycles for Donaldson-Thomas invariants of Calabi-Yau 4-folds: Journal of Algebraic Geometry 32 (2023), 585-639.

51. (with Jinwon Choi and Donggun Lee) Representations on the cohomology of $\overline{\mathcal{M}}_{0,n}$: Advances in Mathematics 435, Part A, December 15 2023, 109364.

52.  (with Donggun Lee) Birational geometry of generalized Hessenberg varieties and the generalized Shareshian-Wachs conjecture: Journal of Combinatorial Theory, Series A 206 (2024), 105884.  

53. Enumerative geometry, before and after string theory: KIAS Springer Series in Mathematics 1, 1~42, Springer 2022. 

54. (with Hyeonjun Park) Virtual fundamental classes of the vanishing loci of cosections: Preprint, submitted to the Proceedings of the workshop in the memory of Bumsig Kim. 

55. (with Hyeonjun Park) Cosection localization via shifted symplectic geometry: In preparation. 

56. (with Donggun Lee) Geometry of the twin manifolds of regular semisimple Hessenberg varieties and unicellular LLT polynomials: To appear in Algebraic Combinatorics. 

Lecture Notes

1. Equivariant cohomology theory. (2008)

2. Geometric invariant theory. (2003)

3. Hyperkahler geometry. (2005)

4. Intersection cohomology of GIT quotients. (2004)

저서 

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