TL;DR
This paper investigates vector bundles on curves with rational tails, providing conditions under which their smoothings result in balanced vector bundles on the general fiber.
Contribution
It offers a new sufficient condition for the general fiber of a smoothing of such curves to be balanced, advancing understanding of vector bundle behavior on complex curves.
Findings
Established a sufficient condition for balanced vector bundles on smoothed curves.
Analyzed the behavior of vector bundles during the smoothing process.
Contributed to the theory of vector bundles on singular and smooth curves.
Abstract
We study vector bundles on curves with rational tails and their smoothings and give a sufficient condition for the general fibre to be balanced.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology