Nathan Chen is a Research

Research Focus

A large part of my research is devoted to studying rational maps between algebraic varieties. These appear in various guises, such as birational invariants called measures of irrationality, (birational) automorphisms and self-maps, and moduli spaces of curves on a given variety.

Recently, I have been thinking about subvarieties of hypersurfaces in projective space.

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Publications & Preprints

Connecting families of curves,
joint with R. Lazarsfeld and F. Moretti.
preprint (2026)·arXiv:2609.20716

Characterizing Varieties Using Birational Transformations,
joint with L. Esser, A. Regeta, C. Urech, and I. van Santen.
preprint (2025)·arXiv:2512.02837

Quadratic points on double planes,
joint with B. Church, H. Pasten, and I. Vogt.
La Matematica (2026)·arXiv:2511.01669·journal

Subvarieties of low degree on general hypersurfaces,
joint with D. Yang.
J. Reine. Angew. Math. (to appear) ·arXiv:2510.11865

A primer on measures of irrationality,
joint with O. Martin.
La Matematica (2026)·arXiv:2509.03783·journal

Curves on complete intersections and measures of irrationality,
joint with B. Church and J. Zhao (an appendix by M. Swaminathan).
J. Eur. Math. Soc. (JEMS) (to appear) ·arXiv:2406.12101

The fibering genus of Fano hypersurfaces,
joint with B. Church, L. Ji, and D. Stapleton.
Alg. Geom. Phys. (to appear) ·arXiv:2308.12401

Group actions and irrationality in surface families,
joint with L. Esser.
Selecta Math. (N.S.) (2025)·arXiv:2410.18427·journal

Nowhere vanishing holomorphic one-forms and fibrations over abelian varieties,
joint with B. Church and F. Hao.
Adv. Math. (2025)·arXiv:2306.15064·journal

Fano hypersurfaces with no finite order birational automorphisms,
joint with L. Ji and D. Stapleton.
Amer. J. Math. (to appear) ·arXiv:2208.07396

Multiplicative bounds for measures of irrationality on complete intersections,
Algebr. Geom. (2024)·arXiv:2111.05549·journal

Rational maps from products of curves to surfaces with p_g = q = 0,
joint with O. Martin.
Math. Z. (2023)·arXiv:2111.08194·journal

Higher index Fano varieties with finitely many birational automorphisms,
joint with D. Stapleton.
Compos. Math. (2022)·arXiv:2110.09568·journal

Rational endomorphisms of Fano hypersurfaces,
joint with D. Stapleton.
Selecta Math. (N.S.) (2024)·arXiv:2103.12207·journal

Nodal elliptic curves on K3 surfaces,
joint with F. Greer and R. Yang.
Math. Ann. (2023)·arXiv:2001.05104·journal

Fano hypersurfaces with arbitrarily large degrees of irrationality,
joint with D. Stapleton.
Forum Math. Sigma (2020)·arXiv:1908.02803·journal

Degree of irrationality of very general abelian surfaces,
Algebra Number Theory (2019)·arXiv:1902.05645·journal

Other writings

Low degree points on singular plane curves,
Columbia REU project, joint with Z. Canale, Z. Curewitz, J. Daum, K. Dovgodko, C. Santiago-Calderón, and S. Yajnik.
Involve (to appear)·arXiv:2603.20529

Measuring the irrationality of abelian surfaces and complete intersections,
PhD thesis, Stony Brook University (2021)·pdf

Curves on surfaces blown up at three points·pdf

Recorded Talks

Higher index Fano varieties in positive characteristic with Bir(X) = 1
May 2023, Simons Center, Stony Brook·video

Rational endomorphisms on Fano hypersurfaces
February 2023, Birational Geometry Seminar, Virtual·video

Curves on very general hypersurfaces
December 2022, Simons Center, Stony Brook·video

Collaborators

My collaborators: