A study of the Hilbert-Mumford criterion for the stability of projective varieties

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dc.creatorRoss, J.
dc.creatorThomas, R. P.
dc.date2004-12-29
dc.date2005-02-02
dc.date.accessioned2026-07-07T07:42:18Z
dc.date.available2026-07-07T07:42:18Z
dc.descriptionWe make a systematic study of the Hilbert-Mumford criterion for different notions of stability for polarised algebraic varieties $(X,L)$; in particular for K- and Chow stability. For each type of stability this leads to a concept of slope $μ$ for varieties and their subschemes; if $(X,L)$ is semistable then $μ(Z)\leμ(X)$ for all $Z\subset X$. We give examples such as curves, canonical models and Calabi-Yaus. We prove various foundational technical results towards understanding the converse, leading to partial results; in particular this gives a geometric (rather than combinatorial) proof of the stability of smooth curves.
dc.description47 pages, 2 figures. Submitted version; typos corrected
dc.identifierhttps://arxiv.org/abs/math/0412519
dc.identifierhttp://arxiv.org/abs/math/0412519
dc.identifierJour. Alg. Geom. 16 (2007), 201--255.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122394
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.subject14L24
dc.titleA study of the Hilbert-Mumford criterion for the stability of projective varieties
dc.typetext

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