ACC for minimal lengths of extremal rays for surfaces
Evgeny Mayanskiy
TL;DR
This paper proves that the lengths of extremal rays in certain Fano surfaces follow the ascending chain condition, confirming a conjecture for the 2-dimensional case.
Contribution
It establishes the ascending chain condition for extremal ray lengths in log canonical Fano surfaces with Picard number one, advancing understanding of their geometric properties.
Findings
Lengths of extremal rays satisfy ACC
Confirms conjecture for 2D Fano surfaces
Advances classification of Fano surfaces
Abstract
We prove that the lengths of extremal rays of log canonical Fano surfaces with Picard number one satisfy the ascending chain condition. This confirms the 2-dimensional case of a conjecture stated by Fujino and Ishitsuka
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Analytic Number Theory Research