Nathan Chen is a Research

Research Interests

Focus Areas

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

Quadratic points on double planes,
joint with Benjamin Church, Hector Pasten, and Isabel Vogt.
preprint (2025)·arXiv:2511.01669

Subvarieties of low degree on general hypersurfaces,
joint with David Yang.
preprint (2025)·arXiv:2510.11865

A primer on measures of irrationality,
joint with Olivier Martin.
preprint (2025)·arXiv:2509.03783

Curves on complete intersections and measures of irrationality,
joint with Benjamin Church and Junyan Zhao (an appendix by Mohan Swaminathan).
preprint (2024)·arXiv:2406.12101

Published Papers

The fibering genus of Fano hypersurfaces,
joint with Benjamin Church, Lena Ji, and David Stapleton.
Algebraic Geometry & Physics (to appear)·arXiv:2308.12401

Group actions and irrationality in surface families,
joint with Louis Esser.
Selecta Mathematica (N.S.) (to appear)·arXiv:2410.18427

Nowhere vanishing holomorphic one-forms and fibrations over abelian varieties,
joint with Benjamin Church and Feng Hao.
Advances in Mathematics (2025)·arXiv:2306.15064·journal

Fano hypersurfaces with no finite order birational automorphisms,
joint with Lena Ji and David Stapleton.
American Journal of Mathematics (to appear)·arXiv:2208.07396

Multiplicative bounds for measures of irrationality on complete intersections,
Algebraic Geometry (2024)·arXiv:2111.05549·journal

Rational maps from products of curves to surfaces with pg = q = 0,
joint with Olivier Martin.
Mathematische Zeitschrift (2023)·arXiv:2111.08194·journal

Higher index Fano varieties with finitely many birational automorphisms,
joint with David Stapleton.
Compositio Mathematica (2022)·arXiv:2110.09568·journal

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

Nodal elliptic curves on K3 surfaces,
joint with François Greer and Ruijie Yang.
Mathematische Annalen (2023)·arXiv:2001.05104·journal

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

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

Other

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

Recent Talks

Videos

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

Invited Talks and Presentations

Algebraic Geometry Northeastern Series (AGNES)
November 2024, Dartmouth College

Thematic Program on Rationality and Hyperbolicity
June 2023, University of Notre Dame

Higher Dimensional Geometry
May 2023, Simons Foundation Conference

Birational Complexity of Algebraic Varieties
December 2022, Stony Brook University

AMS-EMS-SMF Joint Congress of Mathematics
July 2022, Special session on algebraic geometry, Université Grenoble Alpes

AMS Spring Eastern Sectional Meeting
October 2020, Special session on moduli spaces in algebraic and tropical geometry, Tufts University (virtual)

AMS Fall Eastern Sectional Meeting
October 2020, Special session on geometry and arithmetic of algebraic varieties, Pennsylvania State University (virtual)

Colloquium Talks

University of Massachusetts Boston (October 2025)

University of California Santa Barbara (December 2024)

University of California Los Angeles Colloquium (December 2024)

Washington University in St. Louis (November 2024)

Collaborators

Current

My collaborators: