Brylinski-Radon transformation and generic projections

TL;DR

This paper demonstrates that the Brylinski-Radon transformation preserves the perverse sheaf property under generic surjective linear maps from complex vector spaces, revealing new insights into geometric and sheaf-theoretic transformations.

Contribution

It establishes that the pushforward of a perverse sheaf remains perverse under generic surjective linear maps using the Brylinski-Radon transformation, advancing understanding in geometric representation theory.

Findings

Pushforward of perverse sheaves remains perverse under generic surjective linear maps.

The Brylinski-Radon transformation preserves perverse sheaves up to shifts of constant sheaves.

Provides a new proof technique for properties of perverse sheaves under linear transformations.

Abstract

Using the Brylinski-Radon transformation, we prove that under a generic surjective linear map from C^n to C^m, the pushforward of a perverse sheaf is perverse, modulo shifts of constant sheaves.