A looming of phantoms

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

doi:10.1016/j.aim.2026.111046

A looming of phantoms

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	111046
Journal	Advances in Mathematics
Volume	499
DOIs	https://doi.org/10.1016/j.aim.2026.111046
State	Published - Jul 2026

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Algebraic surfaces
Derived categories
Phantom categories

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10.1016/j.aim.2026.111046

Cite this

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title = "A looming of phantoms",

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.",

keywords = "Algebraic surfaces, Derived categories, Phantom categories",

author = "Kimoi Kemboi and Daniel Krashen and Tianle Liu and Yeqin Liu and Eoin Mackall and Svetlana Makarova and Alexander Perry and Robotis, \{Antonios Alexandros\} and Sridhar Venkatesh",

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year = "2026",

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doi = "10.1016/j.aim.2026.111046",

language = "English (US)",

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T1 - A looming of phantoms

AU - Kemboi, Kimoi

AU - Krashen, Daniel

AU - Liu, Tianle

AU - Liu, Yeqin

AU - Mackall, Eoin

AU - Makarova, Svetlana

AU - Perry, Alexander

AU - Robotis, Antonios Alexandros

AU - Venkatesh, Sridhar

PY - 2026/7

Y1 - 2026/7

N2 - 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.

AB - 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.

KW - Algebraic surfaces

KW - Derived categories

KW - Phantom categories

UR - https://www.scopus.com/pages/publications/105039798228

UR - https://www.scopus.com/pages/publications/105039798228#tab=citedBy

U2 - 10.1016/j.aim.2026.111046

DO - 10.1016/j.aim.2026.111046

M3 - Article

AN - SCOPUS:105039798228

SN - 0001-8708

VL - 499

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 111046

ER -

A looming of phantoms

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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