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Lagrangian families of Bridgeland moduli spaces from Gushel–Mukai fourfolds
- Part of
-
- Journal:
- Compositio Mathematica / Volume 161 / Issue 8 / August 2025
- Published online by Cambridge University Press:
- 09 October 2025, pp. 2091-2135
- Print publication:
- August 2025
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- Article
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Let
$X$ be a very general Gushel–Mukai (GM) variety of dimension 
$n\geq 4$, and let 
$Y$ be a smooth hyperplane section. There are natural pull-back and push-forward functors between the semi-orthogonal components (known as the Kuznetsov components) of the derived categories of 
$X$ and 
$Y$. In this paper, we prove that the Bridgeland stability of objects is preserved by both pull-back and push-forward functors. We then explore various applications of this result, such as constructing an eight-dimensional smooth family of Lagrangian subvarieties for each moduli space of stable objects in the Kuznetsov component of a general GM fourfold and proving the projectivity of the moduli spaces of semistable objects of any class in the Kuznetsov component of a general GM threefold, as conjectured by Perry, Pertusi, and Zhao.
