Infinitesimal deformations of cones over transcanonically embedded hyperelliptic curves. (Q1813993)

Let \(\pi:C\to\mathbb{P}^ 1\) be a hyperelliptic curve of genus \(g\), considered as a ramified covering. Let \(K_ 0\) be \(\pi^{- 1}(\text{pt})\), then \((g+1)K_ 0\) is a very ample divisor for every \(\ell>0\), defining the \(\ell\)-th transcanonical projective embedding of \(C\). The embedded curve is projectively normal. Consider the cone \(X\). The purpose of this paper is to compute the graded tangent space of the miniversal deformation of the corresponding singularity. The result is a nice and maybe useful complete table giving \(\dim(T^ 1_{X_{\ell}}(\mu))\) for all \(\ell\) and all \(\mu\).