A Lagrangian sphere which is not a vanishing cycle
Fran\c{c}ois Greer
TL;DR
This paper provides examples of Calabi-Yau threefolds with Lagrangian spheres that are not associated with nodal degenerations, challenging previous assumptions and answering a question posed by Donaldson.
Contribution
It introduces specific examples of Lagrangian spheres in Calabi-Yau threefolds that are not vanishing cycles, addressing a previously open question.
Findings
Existence of Calabi-Yau threefolds with non-vanishing Lagrangian spheres
Counterexamples to the assumption that all Lagrangian spheres are vanishing cycles
Answer to Donaldson's question in the negative
Abstract
We give examples of Calabi-Yau threefolds containing Lagrangian spheres which are not vanishing cycles of nodal degenerations, answering a question of Donaldson in the negative.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry