Kuan-Wen Lai (賴冠文)

I am a postdoc at Academia Sinica. You may consider me as an algebraic geometer. I am currently working on problems related to twisted K3 surfaces, K3 categories of cubic fourfolds, and Gushel–Mukai fourfolds. More about me can be found in my CV. I am currently on the job market.

Papers

In the list below, my papers on finite (algebraic) geometry are grouped together, while my remaining papers are grouped based on the examples they deal with. This isn't really a good way to organize them, as you may find, e.g., that my papers concerning Cremona transformations are spread throughout those groups.

My papers listed in a reverse chronological order can be found in my CV as well as on the arXiv. Before being published on journals, papers on this website will be updated more frequently than those on the arXiv.

Cubic fourfolds and their K3 categories

1. Fourier–Mukai numbers of K3 categories of very general special cubic fourfolds (with Yu-Wei Fan), Israel Journal of Mathematics, accepted. [PDF] [arXiv]
2. New rational cubic fourfolds arising from Cremona transformations (with Yu-Wei Fan), Algebraic Geometry 10 (4) (2023), 432--460. [PDF] [arXiv]
3. New cubic fourfolds with odd degree unirational parametrizations, Algebra & Number Theory, 11 (2017), No. 7, 1597–1626. [PDF] [arXiv]

K3 surfaces and hyperkähler manifolds

1. Nielsen realization problem for derived automorphisms of generic K3 surfaces (with Yu-Wei Fan), preprint. [PDF] [arXiv]
2. On the irrationality of moduli spaces of projective hyperkähler manifolds (with Daniele Agostini and Ignacio Barros), preprint. [PDF] [arXiv]
3. On the irrationality of moduli spaces of K3 surfaces (with Daniele Agostini and Ignacio Barros), Transactions of the American Mathematical Society 376 (2023), No. 2, 1407– 1426. [PDF] [arXiv]
4. Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces (with Masahiro Nakahara), International Mathematics Research Notices 2022, no. 23, 18541–18588. [PDF] [arXiv]
5. Decomposition of Lagrangian classes on K3 surfaces (with Yu-Shen Lin and Luca Schaffler), Mathematical Research Letters 28 (2021), no. 6, 1739–1763. [PDF] [arXiv]
6. Cremona transformations and derived equivalences of K3 surfaces (with Brendan Hassett), Compositio Mathematica, 154 (2018), Issue. 7, 1508–1533. [PDF] [arXiv]

Finite algebraic geometry

1. Frobenius nonclassical hypersurfaces (with Shamil Asgarli and Lian Duan), preprint. [PDF] [arXiv]
2. Transverse linear subspaces to hypersurfaces over finite fields (with Shamil Asgarli and Lian Duan), Finite Fields and Their Applications 95 (2024), Paper No. 102396. [PDF] [arXiv]
3. Bijective Cremona transformations of the plane (with Shamil Asgarli, Masahiro Nakahara, and Susanna Zimmermann), Selecta Mathematica, New Series 28, 53 (2022). [PDF] [arXiv]
4. Transverse lines to surfaces over finite fields (with Shamil Asgarli and Lian Duan), manuscripta mathematica, 165 (2021), 135–157. [PDF] [arXiv] [erratum]

Other writings

• Grothendieck ring of birational permutations — Some thoughts after my paper "Bijective Cremona transformations of the plane". [PDF]
• A tour of the rationality problem of cubic fourfolds — An expository article written for a series of lectures given at Academia Sinica during July 28–August 3, 2021. [PDF]

Recorded talks

• Estimates on the growth of irrationality for moduli spaces of K3 surfaces — A talk at the workshop: Birational Complexity of Algebraic Varieties at Simons Center during December 12–16, 2022. [video]
• Bijective Cremona transformations of the plane — An online talk at National Tsing Hua University on March 21, 2022. [video]