Email: xlzhao at math dot ucsb dot edu
I am an assistant professor at University of California, Santa Barbara. I was a Zelevinsky Research Instructor at Northeastern University, working with Emanuele Macri. I obtained my Ph.D. from University of Michigan in 2015, under the supervision of Herb Clemens and Karen Smith.
- Twisted cubics on cubic fourfolds and stability conditions (joint with Li, Pertusi), arXiv: 1802.01134, submitted.
- On the group of zero-cycles of holomorphic symplectic varieties (joint with Marian), arXiv: 1711.10045.
- Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties (joint with Shen, Yin), arXiv: 1705.06953, submitted.
- The Torelli Theorem for cubic fourfolds (joint with Bayer, Lahoz, Macri, Stellari) - appendix to Stability conditions on Kuznetsov components by Bayer, Lahoz, Macri, Stellari, arXiv: 1703.10839.
- Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces (joint with Li), to appear in Math. Z. (pdf)
- Bridgeland stability conditions on Fano threefolds (joint with Bernardara, Macri, Schmidt), Épijournal de Géométrie Algébrique 1 (2017), Article Nr. 2. (pdf)
- Birational models of moduli spaces of coherent sheaves on the projective plane (joint with Li), to appear in Geometry & Topology. (pdf)
- Nef cones of Hilbert schemes of points on surfaces (joint with Bolognese, Huizenga, Lin, Riedl, Schmidt, Woolf), Algebra & Number Theory 10-4 (2016), 907--930. (pdf)
- Topological Abel-Jacobi mapping and Jacobi inversion, University of Michigan thesis. (pdf)
- The MMP for deformations of Hilbert schemes of points on the projective plane (joint with Li), Algebraic Geometry 5 (3) (2018) 1-35. (pdf)
Holomorphic height pairing and Poincare bundle. This gives a different construction of Clemens' holomorphic height pairing, more close to Hain's approach to the classic height pairing. (pdf)