Osculating behavior of Kummer surface in $\mathbb P^5$

TL;DR

This paper explores the geometric properties of Kummer surfaces in projective 5-space, focusing on their osculating spaces which have dimensions smaller than expected, building on classical and recent results.

Contribution

It analyzes the osculating behavior of Kummer surfaces, connecting historical results with recent developments on hypo-osculating varieties.

Findings

All osculating spaces of the Kummer surface have dimension less than 5.

The paper relates classical results to recent findings on hypo-osculating varieties.

Provides a detailed discussion of geometric properties of Kummer surfaces in projective space.

Abstract

In an article of 1967 W. Edge gave a description of some beautiful geometric properties of the Kummer surface complete intersection of three quadrics in $\mathbb P^5$. Working on it, R. Dye proved that all its osculating spaces have dimension less than the expected 5. Here we discuss these results, also at the light of some recent result about varieties with hypo-osculating behaviour.