All complete intersection varieties are Fano visitors

TL;DR

This paper proves that every smooth complete intersection variety's derived category can be embedded into that of a Fano variety, leading to new invariants and questions in algebraic geometry.

Contribution

It establishes that all smooth complete intersection varieties are Fano visitors, connecting their derived categories to those of Fano varieties for the first time.

Findings

Derived categories of complete intersections embed into Fano varieties' categories

Introduces new invariants for smooth projective varieties

Raises questions about the structure and classification of derived categories

Abstract

We prove that the derived category of a smooth complete intersection variety is equivalent to a full subcategory of the derived category of a smooth projective Fano variety. This enables us to define some new invariants of smooth projective varieties and raise many interesting questions.