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Bibliographic Details
Main Author: Cornea, Robert
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.00164
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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
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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