Nice Initial Complexes of Some Classical Ideals

Details Nice Initial Complexes of Some Classical Ideals Nice Initial Complexes of Some Classical Ideals

2005-12-13

arxiv.org/abs/math/0512283v1

Mathematics

Commutative Algebra

31 pages, 2 figures

Scientific paper

This is a survey article on Gorenstein initial complexes of extensively studied ideals in commutative algebra and algebraic geometry. These include defining ideals of Segre and Veronese varieties, toric deformations of flag varieties known as Hibi ideals, determinantal ideals of generic matrices of indeterminates, and ideals generated by Pfaffians of generic skew symmetric matrices. We give a summary of recent work on the construction of squarefree Gorenstein initial ideals of these ideals when the ideals are themselves Gorenstein. We also present our own independent results for the Segre, Veronese, and some determinantal cases.

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