Conics in Kummer quartics

TL;DR

This paper classifies line and conic configurations in smooth Kummer quartics, establishing an upper bound of 800 conics under specific mapping assumptions, advancing understanding of their geometric structure.

Contribution

It provides a classification of conics in Kummer quartics and establishes a maximum number of 800 conics under certain conditions, which is a new result in algebraic geometry.

Findings

Maximum of 800 conics on such quartics

Classification of line and conic configurations

Assumption that all 16 Kummer divisors map to conics

Abstract

We classify the configurations of lines and conics in smooth Kummer quartics, assuming that all $16$ Kummer divisors map to conics. We show that the number of conics on such a quartic is at most $800$.