The SL(V)-ample cone of product of flag varieties

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• 作者：Ming Shuo Zhou
• 关键词：Semistable ; SL(V) ; ample cone ; Schubert cycle ; 14C17 ; 14L24 ; 14L30
• 刊名：Acta Mathematica Sinica
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：31
• 期：2
• 页码：272-280
• 全文大小：208 KB
• 参考文献：1. Dolgachev, I., Hu, Y.: Variation of geometric invariant theory, with an appendiex by Nicolas Ressayr. / Publ. Math. I.H.E.S., 78, 1-6 (1998)
  2. Fulton, W.: Intersection Theory, Springer, Berlin, 1998 CrossRef
  3. Hartshorne, R.: Algebraic Geometry, Springer, Berlin, 1997
  4. Hu, Y.: Stable configurations of linear subspaces and quotient coherent sheaves. / Q. J. Pure. Appl. Math., 1, 127-46 (2005) CrossRef
  5. Mumford, D., Fogarty, J., Kirwan, E.: Geometric Invariant Theory, 3nd edition, Springer-Verlag, New York, 1994 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

Let k be an algebraically closed field, and V be a vector space of dimension n over k. For a set ω = ( \(\vec d\) (1), ..., \(\vec d\) (m)) of sequences of positive integers, denote by L ω the ample line bundle corresponding to the polarization on the product X = Π i=1 m Flag(V, \(\vec n\) (i)) of flag varieties of type \(\vec n\) (i) determined by ω. We study the SL(V)-linearization of the diagonal action of SL(V) on X with respect to L ω. We give a sufficient and necessary condition on ω such that X ss (L ω) ? \(\not 0\) (resp., X s (L ω) ? \(\not 0\) ). As a consequence, we characterize the SL(V)-ample cone (for the diagonal action of SL(V) on X), which turns out to be a polyhedral convex cone.