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July 2024 Arc scheme and higher differential forms
Yann Le Dréau, Julien Sebag
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Osaka J. Math. 61(3): 381-390 (July 2024).


Let $k$ be a field. In this article, we identify the component of weight 2 of the natural $\mathbf G_{m,k}$-graduation on the $k$-algebra of the arc scheme attached to an affine algebraic variety $X$ with the module of the 2-nd order derivations on $X$. We in particular deduce, from this property, characterizations of the geometry of hypersurfaces (in affine spaces) in terms of the nilpotency on arc scheme.


We are deeply grateful to the anonymous referee whose precise reading and numerous relevant comments have allowed us to broadly improve the presentation of this work.


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Yann Le Dréau. Julien Sebag. "Arc scheme and higher differential forms." Osaka J. Math. 61 (3) 381 - 390, July 2024.


Received: 7 December 2022; Revised: 15 June 2023; Published: July 2024
First available in Project Euclid: 27 June 2024

Primary: 13P10 , 14B05 , 14E15 , 14E18 , 14Q05 , 14Q15 , 14Q20 , 32S05

Rights: Copyright © 2024 Osaka University and Osaka Metropolitan University, Departments of Mathematics

Vol.61 • No. 3 • July 2024
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