For the 2×n rank-1 determinantal variety, the Hilbert series of its second jet scheme equals the cube of the original Hilbert series, specifically ((1+(n-1)z)/(1-z)^(n+1))^3.
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Hilbert series of second order jets of determinantal varieties
For the 2×n rank-1 determinantal variety, the Hilbert series of its second jet scheme equals the cube of the original Hilbert series, specifically ((1+(n-1)z)/(1-z)^(n+1))^3.