Extending symmetric determinantal quartic surfaces

TL;DR

This paper presents an explicit method to extend symmetric determinantal quartic K3 surfaces to Fano 6-folds, revealing a one-to-one correspondence between their moduli and constructing new surfaces of general type.

Contribution

It introduces a novel explicit construction linking quartic K3 surfaces to Fano 6-folds and identifies a 16-parameter family of surfaces of general type within this framework.

Findings

Moduli of 6-fold extensions correspond bijectively to quartic surface moduli.

Constructed a 16-parameter family of surfaces of general type.

Extended symmetric determinantal quartic surfaces to higher-dimensional Fano varieties.

Abstract

We give an explicit construction for the extension of a symmetric determinantal quartic K3 surface to a Fano 6-fold. Remarkably, the moduli of the 6-fold extension are in one-to-one correspondence with the moduli of the quartic surface. As a consequence, we determine a 16-parameter family of surfaces of general type with p_g=1 and K^2=2 as weighted complete intersections inside Fano 6-folds.