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单词 Chow Coordinates
释义

Chow Coordinates

A generalization of Grassmann Coordinates to -D varieties of degree in , where is an -Dprojective space. To define the Chow coordinates, take the intersection of a -D Variety of degree by an -D Subspace of . Then the coordinates of the points of intersectionare algebraic functions of the Grassmann Coordinates of , and by taking a symmetric function of the algebraicfunctions, a hHomogeneous Polynomial known as the Chow form of is obtained. The Chow coordinates are then theCoefficients of the Chow form. Chow coordinates can generate the smallest field of definition of a divisor.


References

Chow, W.-L. and van der Waerden., B. L. ``Zur algebraische Geometrie IX.'' Math. Ann. 113, 692-704, 1937.

Wilson, W. S.; Chern, S. S.; Abhyankar, S. S.; Lang, S.; and Igusa, J.-I. ``Wei-Liang Chow.'' Not. Amer. Math. Soc. 43, 1117-1124, 1996.


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