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- W2183669746 abstract "In 1940, Luis Santalo proved a Helly-type theorem for line transversals to boxes in R d . An analysis of his proof reveals a convexity structure for ascending lines in R d that is isomorphic to the ordinary notion of convexity in a convex subset of R 2di2 . This isomorphism is through a Cremona transformation on the Grassmannian of lines in P d , which enables a precise description of the convex hull and a-ne span of up to d ascending lines: the lines in such an a-ne span turn out to be the rulings of certain classical determinantal varieties. Finally, we relate Cremona convexity to a new convexity structure that we call frame convexity, which extends to arbitrary-dimensional ∞ats in R d ." @default.
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- W2183669746 date "2005-01-01" @default.
- W2183669746 modified "2023-09-26" @default.
- W2183669746 title "CREMONA CONVEXITY, FRAME CONVEXITY," @default.
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