Outdated Archival Version

These pages are not updated anymore. They reflect the state of 22 June 2005. For the current production of this journal, please refer to http://intlpress.com/HHA/.

Extensions of homogeneous coordinate rings to A_µ-algebras

A. Polishchuk

We study $A_{\infty}$-structures extending the natural algebra structure on the cohomology of $\oplus_{n\in\Z} L^n$, 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 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.

Homology, Homotopy and Applications, Vol. 5(2003), No. 1, pp. 407-421

http://www.rmi.acnet.ge/hha/volumes/2003/n1a17/v5n1a17.dvi (ps, dvi.gz, ps.gz, pdf)
ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2003/n1a17/v5n1a17.dvi (ps, dvi.gz, ps.gz, pdf)