Extensions of homogeneous coordinate rings to A∞-algebras

الأصل · EN

We study A∞-structures extending the natural algebra structure on the cohomology of ⊕ₙ Lⁿ, where L is a very ample line bundle on a projective d-dimensional variety X such that Hⁱ(X,Lⁿ)=0 for 0<i<d and all n. We prove that there exists a unique such nontrivial A∞-structure up to homotopy and rescaling. In the case when X is a curve we also compute the group of self-homotopies of this A∞-structure.