Let $G = SL(n)$ be a simple algebraic group over $C$, with $B \subset P \subset G$ a Borel and a parabolic subgroup, respectively. Denote by $P'$ the derived subgroup of $P$, and let $m$ be the Lie algebra of the nilradical of $P$. The nilfibre $N$ is defined as the zero locus of the augmentation ideal $I_+$ of the semi-invariant algebra $I = C[m]^{P'}$. This talk exposes the irreducible components of $N$. To address this, we construct a semi-standard tableau $T^c$, where $c$ its combinatorial datum. This tableau encodes a subspace $u^c\subset m$ defined by the exclusion of certain root vectors. We will show that the closure $\overline{B \cdot u^c}$ is an irreducible component of $N$ and admits an associated Weierstrass section. We provide some evidence that this construction defines an injective map from semi-standard tableaux to irreducible components of $N$, revealing a rich combinatorial structure underlying the geometry of nilfibres and a glimpse of the subjectivity.