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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.00164 |
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| _version_ | 1866915971691708416 |
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| author | Cornea, Robert |
| author_facet | Cornea, Robert |
| contents | This work explores the geometry of stable wild Vafa-Witten bundles over the complex projective plane $\mathbb{P}^2$. Specifically, we consider stable rank-two pairs $(E,Φ)$, with $E\to\mathbb{P}^2$ a rank-two holomorphic vector bundle and $Φ\in H^0(\mathbb{P}^2,\mathrm{End}_0E\otimes\mathcal{O}(d))$ for $d\geq0$, and compute the dimension of the moduli space of such stable pairs. Moreover, we classify stable pairs $(E,Φ)$ when the underlying rank-two bundle $E$ splits or is the push-forward of a line bundle on $\mathbb{P}^1\times\mathbb{P}^1$. Lastly, we examine the fixed point locus of the natural $\mathbb{C}^*$-action on the moduli space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable Wild Vafa-Witten Bundles on the Projective Plane Cornea, Robert Algebraic Geometry This work explores the geometry of stable wild Vafa-Witten bundles over the complex projective plane $\mathbb{P}^2$. Specifically, we consider stable rank-two pairs $(E,Φ)$, with $E\to\mathbb{P}^2$ a rank-two holomorphic vector bundle and $Φ\in H^0(\mathbb{P}^2,\mathrm{End}_0E\otimes\mathcal{O}(d))$ for $d\geq0$, and compute the dimension of the moduli space of such stable pairs. Moreover, we classify stable pairs $(E,Φ)$ when the underlying rank-two bundle $E$ splits or is the push-forward of a line bundle on $\mathbb{P}^1\times\mathbb{P}^1$. Lastly, we examine the fixed point locus of the natural $\mathbb{C}^*$-action on the moduli space. |
| title | Stable Wild Vafa-Witten Bundles on the Projective Plane |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.00164 |