Geodesic
Extensions of homogeneous coordinate rings to $A_{\infty}$-algebras
Homology, homotopy, and applications, Tome 5 (2003) no. 1, pp. 407-421.

Voir la notice de l'article provenant de la source International Press of Boston

We study $A_{\infty}$-structures extending the natural algebra structure on the cohomology of $\oplus_{n\in\mathbb{Z}} L^n$, where $L$ is a very ample line bundle on a projective $d$-dimensional variety $X$ such that $H^i(X,L^n)=0$ for $0 > i > d$ and all $ n \in \mathbb{Z}$. We prove that there exists a unique such nontrivial$A_{\infty}$-structure up to a strict $A_{\infty}$-isomorphism (i.e., an $A_{\infty}$-isomorphism with the identity as the first structure map) and rescaling. In the case when $X$ is a curve we also compute the group of strict $A_{\infty}$-automorphisms of this $A_{\infty}$-structure.
DOI : 10.4310/HHA.2003.v5.n1.a17
Classification : 18E30, 55P43
Keywords: $A_{\infty}$-algebra, $A_{\infty}$-isomorphism, homogeneous coordinate ring 
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A. Polishchuk. Extensions of homogeneous coordinate rings to $A_{\infty}$-algebras. Homology, homotopy, and applications, Tome 5 (2003) no. 1, pp. 407-421. doi : 10.4310/HHA.2003.v5.n1.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2003.v5.n1.a17/

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