# Dimensional interpolation and the Selberg integral

## TL;DR

This paper connects dimensional interpolation in algebraic geometry with Selberg integrals and extends Bessel equations to non-integer orders, revealing new links between geometry, special functions, and monodromy.

## Contribution

It introduces a novel approach to interpolate geometric invariants and special functions to non-integer dimensions, bridging algebraic geometry and analysis.

## Key findings

- Expressed Euler characteristic of line bundles via Selberg integrals.
- Proposed interpolation of higher Bessel equations and their monodromies.
- Linked dimensional interpolation with gamma conjectures in algebraic geometry.

## Abstract

We show that a version of dimensional interpolation for the Riemann--Roch--Hirzebruch formalism in the case of a grassmannian leads to an expression for the Euler characteristic of line bundles in terms of a Selberg integral. We propose a way to interpolate higher Bessel equations, their wedge powers, and monodromies thereof to non--integer orders, and link the result with the dimensional interpolation of the RRH formalism in the spirit of the gamma conjectures.