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February 12, 2026Journal of the London Mathematical Society0 citationsOpen Access

The versal deformation of small resolutions of conic bundles over P1×P1 {P}¹ {P}¹ with two sections blown down

BKBernd KreußlerJSJan Stevens

Key Points

  • This work aims to describe the deformation process of small resolutions of conic bundles into double solids.
  • Focus on twistor spaces over the product of projective spaces.
  • Analyze small resolutions and modifications of conic bundles.
  • Provide explicit descriptions of deformation mechanisms.
  • Establish that twistor spaces can be small resolutions of double solids.
  • Characterize the deformation from conic bundles to double solids.
  • Expand on the general context of these geometric transformations.

Abstract

Abstract Twistor spaces are certain compact complex three‐folds with an additional real fibre bundle structure. We focus here on twistor spaces over . 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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Cite This Study

Kreußler et al. (2026) studied this question.

synapsesocial.com/papers/698d6efe5be6419ac0d54fc1https://doi.org/10.1112/jlms.70443
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