Publications

Published Papers

• Shen, H. Ramirez, T. & Ye, F. (2024). A computational approach to higher Jacobian ideals. Involve - a journal of Mathematics (Accepted).

• Pham, D. & Ye, F. (2024). Left-invariant Hermitian connections on Lie groups with almost Hermitian structures. Glasnik Matematicki Series III, To appear.

• Pham, D. & Ye, F. (2022). Symplectic Lie groups and Double Geometry. Acta Mathematica Universitatis Comenianae, 91(2), 161-190.

• Ye, F., & Zhu, Z. (2020). On Fujita’s freeness conjecture in dimension 5. Advances in Mathematics, 371, 1-56.

• Ye, F., Zhang, T., & Zhu, Z. (2018). Sakai’s theorem for Q-divisors on surfaces and applications. Asian Journal of Mathematics 22(4), 761–786.

• Ye, F., & Zhu, Z. (2017). Global generation of adjoint line bundles on projective 5-folds. Manuscripta Mathematica, 153(3), 545–562.

• Liu, P., Lu, J., & Ye, F. (2017). On lower bounds for slopes of totally ramified triple cover fibrations. Asian Journal of Mathematics, 21, 981–994.

• Amram, M., Cohen, M., Sun, H., Teicher, M., Ye, F., & Zarkh, A. (2015). Combinatorial symmetry of line arrangements and applications. Topology and Its Applications, 193, 226–247.

• Yau, S. S.-T., & Ye, F. (2013). Several splitting criteria for vector bundles and reflexive sheaves. Pacific Journal of Mathematics, 266(2), 449–456.

• Amram, M., Teicher, M., & Ye, F. (2013). Moduli spaces of arrangements of 10 projective lines with quadruple points. Advances in Applied Mathematics, 51(3), 392–418.

• Ye, F. (2013). Classification of moduli spaces of arrangements of nine projective lines. Pacific Journal of Mathematics, 265(1), 243–256.

• Tan, S.-L., Yau, S. S.-T., & Ye, F. (2011). A note on the topology of the complements of fiber-type line arrangements in \(\mathbb{CP}^2\). Pacific Journal of Mathematics, 251.

• Yau, S. S.-T., & Ye, F. (2009). Diffeomorphic types of complements of nice point arrangements in \(\mathbb{CP}^l\). Science in China Series A: Mathematics, 52(12), 2774–2791.

Preprints

• Ye, F. (2024). On the Structure of Second Jacobian Ideals Submitted.

• Pham, D. & Ye, F. (2020). Left invariant complex structures on double Lie groups.

• Amram, M., Cohen, M., Teicher, M., & Ye, F. (2013). Moduli spaces of ten-line arrangements with double and triple points. ArXiv.

Talks and Lectures

• Introduction to \(\mathcal{D}\)-modules, Commutative Algebra & Algebraic Geometry Seminar, CUNY Graduate Center, New York City, March 15, 2019.

• Higher syzygies on Abelian Threefolds, Workshop on Complex Geometry, University of Hong Kong, Hong Kong, July 20, 2018.

• Application of Multiplier Ideals to Geometry and Algebra of Adjoint Line Bundles, Dynamic System and Algebraic Geometry Workshop, Zhejiang University, Hangzhou, China, January 1, 2018

• Multiplier Ideals and Applications to Adjoint Line Bundles, Commutative Algebra & Algebraic Geometry Seminar, CUNY Graduate Center, New York City, October 20, 2017.

• A characterization of big Q-divisors on surfaces and its applications, Commutative Algebra & Algebraic Geometry Seminar, CUNY Graduate Center, New York City, March 3, 2017.

• A non-vanishing theorem for big divisors on surfaces and its applications, Geometry Seminar, University of Hong Kong, Hong Kong, July 6, 2016.

• On base point freeness of adjoint linear systems on projective 5-folds, Math Department Colloquium, Jinan University, Guangzhou, July 1, 2016.

• Okounkov bodies: introduction I & II, Study group on Toric and Spherical Varieties, CUNY Graduate Center, New York, April 4 and 11, 2016.

• Fujita’s Freeness Conjecture on 5-folds, Workshop on Complex Geometry, University of Hong Kong, Hong Kong, July 23, 2015.

• Rational Curves on CP-Manifolds, Working Seminar on Several complex variables and Complex geometry, University of Hong Kong, March 27, 2015.

• Mori Contractions on CP-Manifolds, Working Seminar on Several complex variables and Complex geometry, University of Hong Kong, February 9, 2015.

• Mori’s Theorems on Rational Curves, Working Seminar on Several complex variables and Complex geometry, University of Hong Kong, January 5, 2015.

• Rational Curves on Fano Manifolds with Nef Tangent bundles, Working Seminar on Several complex variables and Complex geometry, University of Hong Kong, February 2, 2015.

• Effective Freeness of Adjoint Linear Systems on 5-folds, Algebraic Geometry Seminar, East China Normal University, Shanghai, September 22, 2014

• Classification of Arrangements of 10 Lines, Complex Geometry, National University of Singapore, Singapore, July 26, 2013

• Global Generation of Adjoint Line Bundles, Young Mathematician Workshop on Arithmetic Algebraic Geometry, East China Normal University, Shanghai, July 9, 2013

• Some Splitting Criteria for Vector Bundles and Reflexive Sheaves, The Hong Kong Mathematical Society Annual General Meeting 2013, Hong Kong, June 8, 2013

• Mori’s existence theorem on rational curves, Working Seminar on Complex Geometry, the University of Hong Kong, Hong Kong, March 5, 2013

• Hirzebruch’s Construction of Ball Quotient Surfaces, Working Seminar on Complex Geometry, the University of Hong Kong, Hong Kong, February 4, 2013

• Effective Freeness of Adjoint Linear Systems, Mini Workshop on Complex Geometry, the University of Hong Kong, Hong Kong, January 10, 2013.

• Irreducibility of Moduli Spaces of Arrangements of Lines, IMR Geometry Seminar, the University of Hong Kong, Hong Kong, July 24, 2012

Research Notes

These notes were created for student seminars and self-study purposes. They may contain typos and errors. Please feel free to email me with any corrections or suggestions.

• Filtrations of Vector Bundles on Smooth Projective Algebraic Curves, 2010 Spring

• Introduction to Invariant Theory and GIT, 2010 Spring

• A Brief Introduction of Characteristic Varieties of Line Arrangements, 2011 Fall.

• Geometry of Cohen-Macaulay Rings, 2012 Spring