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My research focuses on algebraic geometry, which studies the interplay between algebraic equations and the geometric structures they define.
Specifically, I am interested in rationality problems, equivariant birational geometry, and toric geometry.
Publications
Publications
Group actions and irrationality in surface families, by Nathan Chen and Louis Esser, Selecta Math. (N.S.) 31 (2025), no. 5, Paper No. 96. (arXiv)
Rational weighted projective hypersurfaces, by Louis Esser, Int. Math. Res. Not. IMRN 2025 (2025), no. 1, 21-30. (arXiv, pdf, with extra notes)
Exceptional Fano varieties with small minimal log discrepancy, by Louis Esser, Jihao Liu, and Chengxi Wang, Math. Res. Lett. 33 (2026), no. 1, 161-198. (arXiv)
Hypersurfaces with large automorphism groups, by Louis Esser and Jennifer Li, Trans. Amer. Math. Soc. 378 (2025), no. 5, 3667-3698. (arXiv, see here for supporting code)
The dual complex of a G-variety, by Louis Esser, Math. Z. 308, 51 (2024). (arXiv, pdf, with extra notes)
Symmetries of Fano varieties, by Louis Esser, Lena Ji, and Joaquin Moraga, J. Reine Angew. Math. 819 (2025), 89-133. (arXiv)
Log canonical pairs with conjecturally minimal volume, by Louis Esser and Burt Totaro, Manuscripta Math. 175 (2024), 865-895. (arXiv)
Minimal log discrepancies of hypersurface mirrors, by Louis Esser, Forum Math. Sigma 12 (2024), e23. (arXiv, pdf)
Automorphisms of weighted projective space, by Louis Esser, J. Pure Appl. Algebra 228 (2024), no. 6, 107628. (arXiv, pdf, with extra notes)
Calabi-Yau varieties of large index, by Louis Esser, Burt Totaro, and Chengxi Wang, Algebr. Geom., to appear. (arXiv)
Quotient singularities in the Grothendieck ring of varieties, by Louis Esser and Federico Scavia, J. Algebraic Geom. 34 (2025), 183-204. (arXiv)
On explicit birational geometry for minimal n-folds of canonical dimension n-1, by Meng Chen, Louis Esser, and Chengxi Wang, Bull. Lond. Math. Soc. 56 (2024), no. 1, 319-337. (arXiv)
Varieties of general type with doubly exponential asymptotics, by Louis Esser, Burt Totaro, and Chengxi Wang, Trans. Amer. Math. Soc. Ser. B 10 (2023), 288-309. (arXiv)
Optimal sine and sawtooth inequalities, by Louis Esser, Terence Tao, Burt Totaro, and Chengxi Wang, J. Fourier Anal. Appl. 28 (2022), no. 2, Paper No. 14, 21pp. (arXiv)
Non-torsion Brauer groups in positive characteristic, by Louis Esser, Proc. Amer. Math. Soc. 151 (2023), no. 2, 527-531. (arXiv, pdf, with extra notes)
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