Work

The 4-intersection unprojection format

Year: 2025

Type: article

Abstract: Unprojection theory is a philosophy due to Miles Reid, which becomes a useful tool in algebraic geometry for the construction and the study of new interesting geometric objects such as algebraic surfaces and 3-folds. In this present work we introduce a new format of unprojection, which we call the 4-intersection format. It is specified by a codimension 2 complete intersection ideal I which is contained in four codimension 3 complete intersection ideals J 1 , J 2 , J 3 , J 4 and leads to the construction of codimension 6 Gorenstein rings. As an application, we construct three families of codimension 6 Fano 3-folds embedded in weighted projective space which correspond to the entries with identifier numbers 29376, 9176 and 24198 respectively in the Graded Ring Database.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2025.107915

Author: Vasiliki Petrotou

Institution: Hebrew University of Jerusalem

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: University of Ioannina, HORIZON EUROPE Framework Programme, HORIZON EUROPE European Innovation Council