Abstract
Let B be a commutative ring with identity, m, n, and r be positive integers such that r ≤ min{m, n}, a 1, …, a r (resp. b 1, … b r ) be integers such that 1 ≤ a 1< … < a r ≤ m (resp. 1 ≤ b 1 < … < b r < n) and U (resp. V) be the most general m × r (resp. r × n) matrix such that s-minors of first a s − 1 rows (resp. b s − 1 columns) of U (resp. V) are all zero for s = 1, …, r. We investigate the B-algebra C generated by all the entries of UV and all the r-minors of U and V. We introduce a Hodge algebra structure, to which the discrete Hodge algebra associate is Cohen Macaulay, on C and prove that C is Cohen-Macaulay if so is B. Using this Hodge algebra structure, we show that C is the ring of absolute invariants of a certain group action, compute the divisor class group and the canonical class of C, and give a criterion of Gorenstein property of C in terms of a 1 ,…, a r and b 1…, b r .
Published Version
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