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Bibliographic Details
Main Authors:	Mata-Gutiérrez, O., Roa-Leguizamón, L., Torres-López, H.
Format:	Preprint
Published:	2024
Subjects:	Algebraic Geometry
Online Access:	https://arxiv.org/abs/2407.03500
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Table of Contents:

We study the moduli space of coherent systems in $P^2$ using the Segre invariant. We obtain necessary conditions for the existence of $α$-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.