Differential invariants of curves in G(2) flag varieties
Boris Kruglikov, Andreu Llabr\'es
TL;DR
This paper computes the algebra of differential invariants for unparametrized curves in G(2) flag varieties, solving the equivalence problem and relating different cases of parabolic subgroups.
Contribution
It provides the first explicit computation of differential invariants for curves in G(2) flag varieties, addressing the equivalence problem in this context.
Findings
Computed the algebra of differential invariants for G(2) flag varieties
Solved the equivalence problem for unparametrized curves in these varieties
Related the invariants across different parabolic subgroups
Abstract
We compute the algebra of differential invariants of unparametrized curves in the homogeneous G(2) flag varieties, namely in G(2)/P. This gives a solution to the equivalence problem for such curves. We consider the cases of integral and generic curves and relate the equivalence problems for all three choices of the parabolic subgroup P.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Nonlinear Waves and Solitons