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A $t$-intersecting constant dimension subspace code $C$ is a set of$k$-dimensional subspaces in a projective space PG(n,q), where distinctsubspaces intersect in a $t$-dimensional subspace. A classical example of sucha code is the sunflower, where all subspaces pass through the same $t$-space.The sunflower bound states that such a code is a sunflower if $|C| > \left(\frac {q^{k + 1} - q^{t + 1}}{q - 1} \right)^2 + \left( \frac {q^{k + 1} - q^{t+ 1}}{q - 1} \right) + 1$. In this article we will look at the case $t=0$ andwe will improve this bound for $q\geq 9$: a set $\mathcal{S}$ of $k$-spaces inPG(n,q), $q\geq 9$, pairwise intersecting in a point is a sunflower if$|\mathcal{S}|>\left(\frac{2}{\sqrt[6]{q}}+\frac{4}{\sqrt[3]{q}}-\frac{5}{\sqrt{q}}\right)\left(\frac{q^{k + 1} - 1}{q - 1}\right)^2$.

On the sunflower bound for $k$-spaces, pairwise intersecting in a point