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arXiv · 2407.03500

On the Moduli Space of Coherent Systems of Type $(2, c_1, c_2, 2)$ on Projective Plane

O. Mata-Gutiérrez·L. Roa-Leguizamón·H. Torres-López
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Abstract

We study the moduli space of coherent systems in $P^2$ using the Segre invariant. We obtain necessary conditions for the existence of $\alpha$-semistable coherent systems $(E,V)$ of type $(2, c_1, c_2, k)$, with $k \geq 2$. Afterwards, we give numerical conditions to the nonemptiness of the moduli space and compute the critical values depending of the Chern classes. Finally, we give some topological properties of the flips.

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O. Mata-Gutiérrez, L. Roa-Leguizamón, H. Torres-López. 2024-07-03. On the Moduli Space of Coherent Systems of Type $(2, c_1, c_2, 2)$ on Projective Plane. https://arxiv.org/abs/2407.03500

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