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Free, publicly-accessible full text available July 1, 2026
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This is the third in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field K, we prove the arc space analogue of the first and second fundamental theorems of invariant theory for the special linear group. This is more subtle than the results for the general linear and symplectic groups obtained in the first two papers because the arc space of the corresponding affine quotients can be nonreduced.more » « lessFree, publicly-accessible full text available February 1, 2026
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Free, publicly-accessible full text available March 1, 2026
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This is the first in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field [Formula: see text], we construct a standard monomial basis for the arc space of the determinantal variety over [Formula: see text]. As an application, we prove the arc space analogue of the first and second fundamental theorems of invariant theory for the general linear group.more » « less
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