2000/11/30 by Li Chiang, Shi-Shyr Roan
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Geometry and complex manifolds #math.AG #msc:14J30 #msc:14J35 #msc:14M25 #msc:20C30
paper · pdf · doi:10.1155/s0161171204302140
published as IJMMS 2004:48 (2004) 2547-2581 · 27 pages, Latex, 11 figures, Some reorganizations and improvement of presentations, Typos corrected, Arguments of Theorem 1 of section 3 in the earlier version are refined with clearer explanation for the justification of contradicting statement appeared in a published journal literature by some other author
openalex publication_date 2004/01/01 · arxiv created 2004/10/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension n ≥ 4 through the theory of Hilbert scheme of group orbits. For a linear special group G acting on ℂ n , we study the G ‐Hilbert scheme Hilb G ( ℂ n ) and crepant resolutions of ℂ n / G for G the A ‐type abelian group A r ( n ). For n = 4, we obtain the explicit structure of . The crepant resolutions of ℂ 4 / A r (4) are constructed through their relation with , and the connections between these crepant resolutions are found by the “flop” procedure of 4‐folds. We also make some primitive discussion on Hilb G ( ℂ n ) for G the alternating group 𝔄 n +1 of degree n + 1 with the standard representation on ℂ n ; the detailed structure of is explicitly constructed.