We determine explicitly the Hodge ideals for determinant hypersurface as an intersection of symbolic powers determinantal ideals. prove our results by studying and weight filtrations on mixed module $$\mathcal {O}_{\mathscr {X}}(*\mathscr {Z})$$ regular functions space $$\mathscr {X}$$ $$n\times n$$ matrices, with poles along divisor {Z}$$ singular matrices. The composition factors filtration a...

Formulas are obtained in terms of complete reductions for the bigraded components of local cohomology modules of bigraded Rees algebras of 0-dimensional ideals in 2-dimensional Cohen-Macaulay local rings. As a consequence, cohomological expressions for the coefficients of the Bhattacharya polynomial of such ideals are obtained.