This is an announcement for the paper "Notes on the geometry of space of polynomials" by Han Ju Lee. Abstract: We show that the symmetric injective tensor product space $\hat{\otimes}_{n,s,\varepsilon}E$ is not complex strictly convex if $E$ is a complex Banach space of $\dim E \ge 2$ and if $n\ge 2$ holds. It is also reproved that $\ell_\infty$ is finitely represented in $\hat{\otimes}_{n,s,\varepsilon}E$ if $E$ is infinite dimensional and if $n\ge 2$ holds, which was proved in the other way by Dineen. Archive classification: math.FA Mathematics Subject Classification: 46B20 The source file(s), Notes-on-geometry-polynomials-revised.tex: 12189 bytes, is(are) stored in gzipped form as 0708.0331.gz with size 4kb. The corresponding postcript file has gzipped size 53kb. Submitted from: hahnju@postech.ac.kr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0708.0331 or http://arXiv.org/abs/0708.0331 or by email in unzipped form by transmitting an empty message with subject line uget 0708.0331 or in gzipped form by using subject line get 0708.0331 to: math@arXiv.org.