Objects of a Phantom on a Rational Surface

2025/10/30 by Mattoo, Amal · 1 citation
#14F08 (Primary) 14J26 #18G80 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.26107

Abstract

Johannes Krah showed that the blowup of P² in 10 general points admits a phantom subcategory. We construct three types of objects in such a phantom: a strong generator, projections of skyscraper sheaves, and a family of objects with two nonzero cohomology sheaves. We study the deformation theory of these objects to show that the phantom contains rich geometry, such as encoding the blowdown map to P². We also show that there exists a co-connective dg-algebra whose derived category is a phantom.

Citations

• Some remarks about deformation theory and formality conjecture
• Homogeneous Interpolation and Some Continued Fractions
• Homogeneous interpolation on ten points
• Quasi-homogeneous linear systems on P2 with base points of multiplicity 7, 8, 9, 10

Cited by

• A new phantom on a rational surface

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