Stability under Fourier-Mukai transforms on elliptic surfaces

Abstract: Let $X$ be a Weierstrass elliptic surface. By moving the polarization towards the fiber direction while keeping the volume of the polarization fixed, we can define a notion of limit Bridgeland stability. In this talk, we will prove that under certain conditions the relative Fourier--Mukai transform of a slope semistable sheaf is a limit semistable object. In the case that the surface has Picard rank two, a detailed study of the potential Bridgeland walls will provide us with extra numerical conditions to guarantee that the Fourier--Mukai transform of a 1-dimensional slope semistable sheaf is Bridgeland semistable.

algebraic geometry

Audience: researchers in the topic

Comments: Zoom Meeting ID: 913 6913 4478

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Brazilian algebraic geometry seminar

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