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arXiv · 2409.12022

The versal deformation of small resolutions of conic bundles over $\mathbb{P}^1\times\mathbb{P}^1$ with two sections blown down

Bernd Kreussler·Jan Stevens
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Abstract

Twistor spaces are certain compact complex threefolds with an additional real fibre bundle structure. We focus here on twistor spaces over $3\mathbb{C}\mathbb{P}^2$. Such spaces are either small resolutions of double solids or they can be described as modifications of conic bundles. The last type is the more special one: they deform into double solids. We give an explicit description of this deformation, in a more general context.

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Bernd Kreussler, Jan Stevens. 2024-09-18. The versal deformation of small resolutions of conic bundles over $\mathbb{P}^1\times\mathbb{P}^1$ with two sections blown down. https://doi.org/10.1112/jlms.70443

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