Raymond Cheng

Writings

Collected here is the writing that I have done over the various years.

Publications and Preprints

  1. Free curves in Fano hypersurfaces must have high degree.
    To appear in Proc. Am. Math. Soc.
    (arXiv | doi | pdf)
  2. Derived categories of quartic double fivefolds,
    with Alex Perry, and Xiaolei Zhao.
    To appear in IMRN.
    (arXiv | doi | pdf)
  3. \(q\)-bic threefolds and their surface of lines.
    Preprint.
    (arXiv | pdf)
  4. \(q\)-bic hypersurfaces and their Fano schemes.
    Pure Appl. Math. Q. 21 (2025), no. 4, 1721-1773.
    (arXiv | doi | pdf)
  5. \(q\)-bic forms.
    J. Algebra. 675C (2025), 196-236.
    (arXiv | doi | pdf)
  6. Projectivity of the moduli of curves,
    with Carl Lian, and Takumi Murayama.
    Stacks Project Expository Collection, 1–43, London Math. Soc. Lecture Note Ser., 480, Cambridge Univ. Press, Cambridge, 2022.
    (doi | pdf)
  7. Theorem of the Base,
    with Lena Ji, Matt Larson, and Noah Olander.
    Stacks Project Expository Collection, 163–193, London Math. Soc. Lecture Note Ser., 480, Cambridge Univ. Press, Cambridge, 2022.
    (doi | pdf)
  8. Unbounded negativity on rational surfaces in positive characteristic,
    with Remy van Dobben de Bruyn.
    J. Reine Angew. Math. 783 (2022), 217–226.
    (arxiv | doi | pdf)
  9. Combinatorial iterated integrals and the harmonic volume of graphs,
    with Eric Katz.
    Adv. in Appl. Math. 128 (2021), 102190, 23 pp.
    (arXiv | doi | pdf)
  10. Combinatorial aspects of the quantized universal enveloping algebra of \(\mathfrak{sl}_{n+1}\),
    with David Jackson and Geoff Stanley.
    Ann. Comb. 22 (2018), no. 4, 681–710.
    (arXiv | doi | pdf)

Dissertation