On the Moduli Space of Coherent Systems of Type $(2, c_1, c_2, 2)$ on Projective Plane
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909241464324096 |
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| author | Mata-Gutiérrez, O. Roa-Leguizamón, L. Torres-López, H. |
| author_facet | Mata-Gutiérrez, O. Roa-Leguizamón, L. Torres-López, H. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Moduli Space of Coherent Systems of Type $(2, c_1, c_2, 2)$ on Projective Plane Mata-Gutiérrez, O. Roa-Leguizamón, L. Torres-López, H. Algebraic Geometry 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. |
| title | On the Moduli Space of Coherent Systems of Type $(2, c_1, c_2, 2)$ on Projective Plane |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.03500 |