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arXiv · 1407.5025

A cohomological interpretation of derivations on graded algebras

Xia Liao·Mathias Schulze
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Abstract

We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$-algebras $A$ and normal projective $k$-varieties $X$ equipped with an ample $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $D$. We obtain a generalized Euler sequence involving a sheaf on $X$ whose space of global sections consists of all homogeneous $k$-linear derivations of $A$ and a sheaf of logarithmic derivations on $X$.

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Xia Liao, Mathias Schulze. 2017-09-20. A cohomological interpretation of derivations on graded algebras. https://doi.org/10.1007/s13366-017-0357-3

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