Affine Spaces within Projective Spaces
Andrea Blunck, Hans Havlicek

TL;DR
This paper explores the structure of affine spaces formed within projective spaces by complements of a fixed subspace, characterizing certain lines as reguli and applying these ideas to dual spreads without finite-dimensional or pappian assumptions.
Contribution
It introduces a novel affine space structure within projective spaces and characterizes lines as reguli, extending the theory beyond finite-dimensional or pappian spaces.
Findings
Certain lines are affine reguli or cones over reguli
The affine space structure aids in describing dual spreads
Results hold without finite-dimensional or pappian assumptions
Abstract
We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our concepts to the problem of describing dual spreads. We do not assume that the projective space is finite-dimensional or pappian.
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