Quartic K3 surfaces and Cremona transformations

TL;DR

This paper demonstrates that certain automorphisms of smooth quartic K3 surfaces cannot be obtained from Cremona transformations of the surrounding projective space, answering a longstanding question.

Contribution

It establishes the existence of automorphisms of quartic K3 surfaces that are not induced by Cremona transformations, providing new insights into surface automorphisms.

Findings

Existence of non-Cremona automorphisms of quartic K3 surfaces

Negative answer to Giz.atullin's question

Advances understanding of K3 surface automorphisms

Abstract

We prove that there is a smooth quartic K3 surface automorphism that is not derived from the Cremona transformation of the ambient three-dimensional projective space. This gives a negative answer to a question of Professor Marat Giz.atullin