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Hodge Ideals for the Determinant Hypersurface by Michael Perlman; Claudiu Raicu is a Mathematics article available to read on EtoBox.

What is Hodge Ideals for the Determinant Hypersurface about?

We determine explicitly the Hodge ideals for the determinant hypersurface as an intersection of symbolic powers of determinantal ideals. We prove our results by studying the Hodge and weight filtrations on the mixed Hodge module O X ( \* Z ) of regular functions on the space X of n × n matrices, with poles along the divisor Z of singular matrices. The composition factors for the weight filtration on O X ( \* Z ) are pure Hodge modules with underlying D-modules given by the simple GL-equivariant D-modules on X , where GL is the natural group of symmetries, acting by row and column operations on the matrix entries. By taking advantage of the GL-equivariance and the Cohen-Macaulay property of their associated graded, we describe explicitly the possible Hodge filtrations on a simple GL-equivariant D-module, which are unique up to a shift determined by the corresponding weights. For non-square matrices, O X ( \* Z ) is replaced by the local cohomology modules H • Z (X , O X ), which turn out to be pure Hodge modules. By working out explicitly the Decomposition Theorem for some natural resolutions of singularities of determinantal varieties, and using the results on square matrices, we d

Who reads Hodge Ideals for the Determinant Hypersurface?

Author

Michael Perlman; Claudiu Raicu

Publisher

Springer Science and Business Media LLC

Published

2021

Language

EN

Field

Mathematics (Physical Sciences)