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A study of the Hilbert-Mumford criterion for the stability of projective varieties | J. Ross
; R. P. Thomas
; | Date: |
29 Dec 2004 | Subject: | Algebraic Geometry; Differential Geometry MSC-class: 14L24 | math.AG math.DG | Abstract: | We 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 $mu$ for varieties and their subschemes; if $(X,L)$ is semistable then $mu(Z)lemu(X)$ for all $Zsubset X$. 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. | Source: | arXiv, math.AG/0412519 | Services: | Forum | Review | PDF | Favorites |
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