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arXiv · 1805.02616

An observation on the Poincar\'e polynomials of moduli spaces of one-dimensional sheaves

Oleksandr Iena
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Abstract

We notice that for $0<d\le 6$ the Poincar\'e polynomial of Simpson moduli space $M_{dm + 1}(\mathbb P_2)$ is divisible by the Poincar\'e polynomial of the projective space $\mathbb P_{3d-1}$. A somehow regular behaviour of the difference of the Poincar\'e polynomials of the Hilbert scheme of $\frac{(d-2)(d-1)}{2}$ points on $\mathbb P_2$ and the moduli space of Kronecker modules $N(3; d-2, d-1)$ is noticed for $d=4, 5, 6$.

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Oleksandr Iena. 2018-05-07. An observation on the Poincar\'e polynomials of moduli spaces of one-dimensional sheaves. https://arxiv.org/abs/1805.02616

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