Definition of sharpe ratio maximising and variance minimising portfolios

In this paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2226985, in the derivation of the mean variance efficient portfolio using lagrangians in the appendix, on page 29, the two portfolios are defined:

$$
pi_R=frac{V^{-1}R}{1^TV^{-1}R}, quad pi_sigma=frac{V^{-1} 1}{1^TV^{-1}1}
$$
where $V$ is the covariance matrix, $R$ is a column vector of returns and $1$ is the vector of ones. $pi_R$ is said to be the portfolio that maximises the sharpe ratio while $pi_sigma$ is the portfolio that minimises variance, I’m not quite sure how the definitions follow?

Update: For background:If we let $d$ be a column vector of active weights, that is, the difference between the portfolio weight and the benchmark, then the objective is to:
$$
text{max} ~~R^T d
$$
subject to
$$
d^T V d = sigma^2_alpha, quad 1^Td =0
$$
where $sigma^2_alpha$ is the active portfolios variance of arithmetic return.

Setting up the lagrangian and a bit of calculus gets to:
$$
d=frac{1}{2lambda_1} left( V^{-1}R – left(frac{1^TV^{-1}R}{1^TV^{-1}1} right)V^{-1} 1right)
$$
this is the last step before the portfolios are defined.