Finiteness of Calabi-Yau quasismooth weighted complete intersections

TL;DR

This paper proves that for each fixed dimension, there are only finitely many families of Calabi-Yau quasismooth weighted complete intersections, extending previous finiteness results to higher codimensions.

Contribution

It generalizes Johnson and Kollár's finiteness result to higher codimensions for Calabi-Yau quasismooth weighted complete intersections.

Findings

Finiteness of families for fixed dimension established

Extension of previous results to higher codimensions

Supports classification efforts in algebraic geometry

Abstract

We prove that there exist only finitely many families of Calabi-Yau quasismooth weighted complete intersections with every fixed dimension $m$. This generalizes a result of Johnson and Koll\'{a}r to higher codimensions.