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DTSTART:20250101T000000
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DTSTART;TZID=Asia/Seoul:20260226T160000
DTEND;TZID=Asia/Seoul:20260226T170000
DTSTAMP:20260506T150514
CREATED:20260219T171800Z
LAST-MODIFIED:20260219T171938Z
UID:4438-1772121600-1772125200@ccg.ibs.re.kr
SUMMARY:On Slope Unstable Fano varieties
DESCRIPTION:    Speaker\n\n\nYen-An Chen\nKIAS\n\n\n\n\n\n\nFor Fano varieties\, significant progress has been made recently in the study of K-stability\, while the understanding of the weaker but more algebraic concept of $(−K)$-slope stability remains intricate. For instance\, a conjecture attributed to Iskovskikh states that the tangent bundle of a Picard rank one Fano manifold is slope stable. Peternell-Wisniewski and Hwang proved this conjecture up to dimension five in 1998\, but Kanemitsu later disproved it in 2021. To address this gap in understanding\, we present a method that aims to characterize the geometry associated with the maximal destabilizing sheaf of the tangent sheaf of a Fano variety. This approach utilizes modern advancements in the foliated minimal model program. In dimension two\, our approach leads to a complete classification of $(−K)$-slope unstable weak del Pezzo surfaces with canonical singularities. As by-products\, we provide the first conceptual proof that $\mathbb{P}^1 \times \mathbb{P}^1$ and $\mathbb{F}_1$ are the only $(−K)$-slope unstable nonsingular del Pezzo surfaces\, recovering a classical result of Fahlaoui in 1989. This is the joint work with Ching-Jui Lai.
URL:https://ccg.ibs.re.kr/event/on-slope-unstable-fano-varieties/
LOCATION:B236\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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