Research

My research is primarily concerned with geometric structures on algebraic varieties, especially moduli problem of curves and sheaves. In particular, my interests include:

• • Rationality of moduli of stable sheaves.

  • Higgs and co-Higgs sheaves

• • Globally generated vector bundles.

  • Hyperplane arrangements and logarithmic bundles with the Torelli problem.

  • Arithmetically Cohen-Macaulay sheaves / Ulrich sheaves

  • Hilbert scheme of curves

  • Toric varieties and toric sheaves

Ph.D. Thesis : Moduli spaces of stable sheaves on the projective plane and on the plane quartic curve (2007),   Univ. Mchigan, Ann Arbor, 

                        supervised by Prof. Igor Dolgachev

Papers

• Virtual Poincare polynomial of moduli space of semistable sheaves of rank two on reducible curve, with D. Lim and S.-B. Yoo, submitted. 

• Net logarithmic tangent sheaves of complete intersection, with M. Jeong, submitted.

• Counting aCM toric vector bundles of rank two on the Veronese surfaces, with Y. Hong, to appear in Alg. Rep. Theory. 

• Rational curves in a quadric threefold via a SL(2,C)-representation, with K. Chung and S. Yoo, J. Kor. Math. Soc. 62 (2025), no. 4, 771-790. 

• A quick journey to stable sheaves and vector bundles, with F. Malaspina, Bolletino dell'Unione Matematica Italiana 18 (2025), 829-851.

• Logarithmic vector bundles on the blown-up variety, with M. Jeong, Results in Math. 79 (2024), no. 4. 

• Generalized logarithmic sheaf on smooth projective surfaces, with S. Marchesi, J. Pons-Llopis and J. Valles, Int. Math. Res. Notices (2023) no. 21, 18387-18442. 

• Hypersurface arrangement of aCM type, with E. Ballico, Mathematische Nachrichten 295 (2022), no. 2, 242-258. 

• ACM vector bundles on projective surfaces of nonnegative Kodaira dimension, with E. Ballico and J. Pons-Llopis, Int. J. Math. 32 (2021), no. 14, 2150109.

• Representation type of surfaces in P3, with E. Ballico,  J. Math. Soc. Japan 72 (2020), no. 4, 1097-1118. 

• Curves in Segre threefolds, with E. Ballico and K. Chung, Forum Mathematicum 32 (2020), no. 1, 63-78. 

• Ulrich bundles on smooth projective varieties of minimal degree, with M. Aprodu, F. Malaspina and J. Pons-Llopis, Proc. Amer. Math. Soc. 147 (2019), no. 12, 5117-5129. 

• Existence of nontrivial logarithmic co-Higgs structure on curves, with E. Ballico, Int. J. Math. 30 (2019), no. 5, 26 pages. 

• ACM sheaves on the double plane, with E. Ballico, F. Malaspina and J. Pons-Llopis, Trans. Amer. Math. Soc. 372 (2019), no. 3, 1783-1816.

• 2-nilpontent co-Higgs structures, with E. Ballico, Manuscripta Mathematica 159 (2019), May, no. 1~2, 39-56.

• Logarithmic co-Higgs bundles, with E. Ballico, Mediterranean J. Math. 16 (2019), no. 1, Article 9.

• Double lines on quadric hypersurfaces, with E. Ballico, Tohoku Math. J. 70 (2018), 447-473. 

• A note on co-Higgs bundles, with E. Ballico, Taiwanese J. Math. 21 (2017), no. 2, 267-281.

• ACM vector bundles of rank two on reducible hyperquadrics, with E. Ballico and J. Pons-Llopis, J. Algebra 489 (2017), 73-90.

• Globally generated vector bundles on complete intersection Calabi-Yau threefolds, with E. Ballico and F. Malaspina, Adv. Theo. Math. Phys. 20 (2016), no. 5, 1125-1166.

• On higher rank globally generated vector bundles over a smooth quadric threefold, with E. Ballico and F. Malaspina, Proc. Edinb. Math. Soc. 59 (2016), no. 2, 311-337 .

• Globally generated vector bundles on the Segre threefold with Picard number two, with E. Ballico and F. Malaspina, Math. Nachr. 289 (2016), no. 5-6, 523-536.

• Globally generated vector bundles on P1*P1*P1, with E. Ballico and F. Malaspina, J. Algebra 450 (2016), 487-521.

• A Torelli type problem for logarithmic bundles over projective varieties, with E. Ballico and F. Malaspina, Quart. J. Math. 66 (2015), no. 2, 417-436.

• Globally generated vector bundles on a smooth quadric surface, with E. Ballico and F. Malaspina, Sci. Math. China 58 (2015), no. 3, 633-652.

• Stable sheaves on a smooth quadric surface with linear Hilbert bipolynomial, with E. Ballico, The Scientific World Journal (2014) Article ID 346126, 10 pages.

• Reflexive and spanned sheaves on P3, with E. Ballico and F. Malaspina, Results in Math. 65 (2014), no. 1-2, 27-47.

• Globally generated vector bundles of rank 2 on a smooth quadric threefold, with E. Ballico and F. Malaspina, J. Pure Appl. Algebra 218 (2014), no. 2, 197-207.

• Cubic symmetroids and vector bundles on a smooth quadric surface, C. R. Math. Acad. Sci. Paris 351 (2013), no. 13-14, 557-560.

• Moduli of stable sheaves on a smooth quadric and a Brill-Noether locus, J. Pure Appl. Algebra 215 (2011), no. 9, 2099-2105.

• On triple Veronese embeddings of Pn in the Grassmannians, Math. Nachr. 284 (2011), no. 11-12, 1453-1461.

• Jumping conics on a smooth quadric in P3, Ann. Mat. Pura Appl. 190 (2011), no. 2, 195-208.

• Dominance of a rational map to the Coble quartic, Proc. Amer. Math. Soc. 138 (2010), no. 3, 777-786.

• A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4, Cent. Eur. J. Math. 7 (2009), no. 4, 617-622.

Talks

• Resolving a rational map on the space of plane cubics, Conference on recent progress in algebraic geometry, East China University, Shanghai (2025.10.15-2025.10.19)

• On a rational self-map of the projective space of plane cubic curves, JJAG5 algebraic geometry in Korea, ShillaStay in Cheonan (2025.09.17-2025.09.20)

• The net logarithmic tangent sheaves of complete intersection, YeungNam workshop on algebraic geometry XIV, DGIST (2025.05.02-2025.05.03)

• Logarthmic sheaf and Torelli problem, Korea-Japan conference on algebraic geometry, IBS CCG (2023.02.13-2023.02.17)

• Logarithmic sheaf and Torelli problem, Conference 'Vector bundles and Chennai', IIT Madras (2023.02.06-2023.02.11)

• Torelli problem on logarithmic sheaves, ZAG (online), (2022.01)

• Generalized logarithmic sheaf and its Torelli problem, Conference: algebraic geometry in Ischia for Alexandru Dimca's retirement, Ischia (2021.10.11-2021.10.14)

• Globally generated vector bundles on the complete intersection Calabi-Yau threefolds, IMPANGA15, Bedlewo (2015.04)

• Hilbert scheme of locally CM curves in Segre threefold, Workshop on projective geometry and syzygies, IMPAN (2015.04)

• Classification of globally generated vector bundles, University of Warwick (2015.02)

• Schwarzenberger bundles and the self-duality of the Coble quartic, Summer school on mirror symmetry, KIAS, Anmyundo (2011.06)

• Restriction maps to the Coble quartic, algebraic geometry seminar, University of Tokyo (2011.01)

• Jumping conics on a smooth quadric surfaces, Conference on algebraic surfaces and related topics, POSTECH, Pohang (2009.08)

• Using restriction maps between moduli spaces, GAeL 2009, Lorentz center, Leiden (2009.06)

• The rationality problem of the Coble quartic, Vortrage zum Graduiertenkolleg 1463, Leibniz University Hannover (2008.07)

• Brill-Noether loci of the Coble quartics, Oberseminar, Algebraische Geometrie, University of Zurich (2007.05)

Conferences organizing

• Workshop of classical moduli theory and its related topics (2025.11.20-2025.11.22), Kyungbuk National University, Daegu.

• ??

• Ulrich sheaves and syzygies (2016.09.05-2016.09.09), Bloomvista Hotel, Yangpyeong. 

Ph.D. students

• Min-Gyo Jeong (2025), thesis title: Logarithmic vector bundles and the Torelli problem on smooth projective varieties

• Yeonjae Hong, Dongsun Lim