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Rationality of the universal K3 surface of genus 8

Research paper by Daniele Di Tullio

Indexed on: 26 May '20Published on: 24 May '20Published in: arXiv - Mathematics - Algebraic Geometry



Abstract

The aim of the present paper is to prove the rationality of the universal family of polarized $ K3 $ surfaces of degree 14. This is achieved by identifying it with the moduli space of cubic fourfolds plus the data of a quartic scroll. The last moduli space is finally proved to be rational since it has a natural structure of $\mathbb P^n$-bundle over a $ k $-stably rational variety with $k \leq n$.