A note on d-sequences and regular sequences of quadrics

Let K be a field and X , Y denote matrices such that the entries of X are either indeterminates over K or 0, not all zero, and the entries of Y are indeterminates over K which are different from those appearing in X . We consider the ideal I 1 ( X Y ) , which is the ideal generated by the homogeneou...

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Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2022-12, Vol.132 (2)
Main Authors: Saha, Joydip, Sengupta, Indranath, Tripathi, Gaurab
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let K be a field and X , Y denote matrices such that the entries of X are either indeterminates over K or 0, not all zero, and the entries of Y are indeterminates over K which are different from those appearing in X . We consider the ideal I 1 ( X Y ) , which is the ideal generated by the homogeneous polynomials of degree 2 given by the 1 × 1 minors of the matrix XY . We prove that d -sequences and regular sequences arise naturally as part of generators of I 1 ( X Y ) for some special cases. We use this information to calculate the equations defining the Rees algebra of I 1 ( X Y ) .
ISSN:0973-7685
DOI:10.1007/s12044-022-00719-x