Sheaf theoretic compactifications of the space of rational quartic plane curves

Let $R_4$ be the space of rational plane curves of degree $4$. In this paper, we obtain a sheaf theoretic compactification of $R_4$ via the space of $α$-semistable pairs on $\mathbb{P}^2$ and its birational relations through wall-crossings of semistable pairs. We obtain the Poincaré polynomial of the compactified space.

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