Cremona convexity, frame convexity and a theorem of Santal Academic Article

abstract

• Abstract In 1940, Luis Santal proved a Helly-type theorem for line transversals to boxes in d . An analysis of his proof reveals a convexity structure for ascending lines in d that is isomorphic to the ordinary notion of convexity in a convex subset of 2d2. This isomorphism is through a Cremona transformation on the Grassmannian of lines in d , which enables a precise description of the convex hull and affine span of up to d ascending lines: the lines in such an affine 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 flats in d .

authors

• Sottile, Frank

published proceedings

• Advances in Geometry

author list (cited authors)

• Goodman, J. E., Holmsen, A., Pollack, R., Ranestad, K., & Sottile, F.

citation count

• 4

complete list of authors

• Goodman, JE||Holmsen, A||Pollack, R||Ranestad, K||Sottile, F

publication date

• January 2006

publisher

• DE GRUYTER  Publisher

published in

• Advances in Geometry  Journal

Digital Object Identifier (DOI)

• 10.1515/advgeom.2006.018

start page

• 301

end page

• 321

volume

• 6

issue

• 2

URL

• http://dx.doi.org/10.1515/advgeom.2006.018