A Looming of phantoms

Kimoi Kemboi; Daniel Krashen; Tianle Liu; Yeqin Liu; Eoin Mackall; Svetlana Makarova; Alexander Perry; Antonios-Alexandros Robotis; Sridhar Venkatesh

arXiv · 2511.05381

A Looming of phantoms

Kimoi Kemboi·Daniel Krashen·Tianle Liu·Yeqin Liu·Eoin Mackall·Svetlana Makarova·Alexander Perry·Antonios-Alexandros Robotis·Sridhar Venkatesh

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Abstract

Following Krah's method, we construct new examples of phantom categories as semiorthogonal components of the derived categories of two types of rational surfaces: the blowup of the plane at 11 points in general position, and the blowup of the second Hirzebruch surface at 9 points in general position. We also pose conjectures about the existence of phantom subcategories in the derived categories of other rational surfaces, obtained as the blowups of the other Hirzebruch surfaces.

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Kimoi Kemboi, Daniel Krashen, Tianle Liu, Yeqin Liu, Eoin Mackall, Svetlana Makarova, Alexander Perry, Antonios-Alexandros Robotis, Sridhar Venkatesh. 2025-11-07. A Looming of phantoms. https://arxiv.org/abs/2511.05381

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