d-sequence and Regular sequence of Quadrics

2017/03/06 by Saha, Joydip, Sengupta, Indranath, Tripathi, Gurab
#13P10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13C40

paper · doi:10.48550/arxiv.1703.01756

Abstract

Let K be a field and X, Y denote matrices such that, the entries of X are either indeterminates over K or 0 and the entries of Y are indeterminates over K which are different from those appearing in X. We consider ideals of the form I₁(XY), 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 I₁(XY) for some special cases. We use this information to calculate the equations defining the Rees algebra of I₁(XY).

Related

• ASL structures of some quadrics
• Some classes of sequences of Linear Type
• Rees algebras of ideals submaximally generated by quadrics
• Ideals generated by quadrics
• Rees algebra and almost linearly presented ideals in three variables