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From nice ideals to nice initial complexesAlgebra & Discrete Mathematics
|Speaker: ||Serkan Hosten, San Francisco State University|
|Location: ||693 Kerr|
|Start time: ||Mon, Apr 4 2005, 3:10PM|
In this joint work with Aldo Conca and Rekha Thomas, we concentrate on
defining ideals of Segre products, Veronese embeddings, determinantal
varieties, and other toric varieties. These classical objects have very nice
properties, like being Cohen-Macaulay. In many cases there are
characterizations when further nice properties hold (for instance,
Gorenstein-ness). We ask the following fundamental question:
when are such nice properties inherited by an initial ideal?
As an example, take the case of Gorenstein Segre products or Veronese. embeddings. In both cases we construct initial complexes that are also
Gorenstein. We also describe shellings of these complexes.