Non-existence of phantoms on some non-generic blowups of the projective
 plane

Lev Borisov; Kimoi Kemboi

doi:10.48550/arxiv.2405.01683

May 2, 2024Open Access

Non-existence of phantoms on some non-generic blowups of the projective plane

View Full Paper

Ask AI

Bookmark

Share

Key Points

Blowups of the projective plane at points positioned along a smooth cubic curve do not contain phantoms, provided the points maintain a very general position on the curve.
Theoretical analysis of geometric configurations proves that non-generic blowups avoid phantom categories, using point arrangements in very general position on a smooth cubic curve.
Highlights structural limitations on derived categories of algebraic surfaces, establishing that these specific blowups of the projective plane cannot host phantom subcategories.

Implication

Theoretical analysis reveals the absence of phantoms on projective plane blowups along a smooth cubic curve, indicating strong geometric constraints on derived categories.

Abstract

We show that blowups of the projective plane at points lying on a smooth cubic curve do not contain phantoms, provided the points are chosen in very general position on this curve.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Borisov et al. (2024) studied this question.

synapsesocial.com/papers/68e6beabb6db64358763efb0 https://doi.org/10.48550/arxiv.2405.01683

View Full Paper

Ask AI

Bookmark

Share

Non-existence of phantoms on some non-generic blowups of the projective plane

Key Points

Implication

Abstract

Discussion

Cite This Study

Non-existence of phantoms on some non-generic blowups of the projective plane

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

More related papers

Keep reading

More related papers