A remark on generalized complete intersections

TL;DR

This paper clarifies and explicates the construction of generalized complete intersections, especially in the context of Calabi-Yau threefolds, using Cech cohomology, providing insights into non-complete intersection subvarieties.

Contribution

It offers a new perspective on generalized complete intersections by employing standard Cech cohomology, making their construction more explicit and understandable.

Findings

Explicit Cech cohomology description of generalized complete intersections

Worked example of a generalized complete intersection Calabi-Yau threefold

Enhanced understanding of non-complete intersection subvarieties

Abstract

We observe that an interesting method to produce non-complete intersection subvarieties, the generalized complete intersections from L. Anderson and coworkers, can be understood and made explicit by using standard Cech cohomology machinery. We include a worked example of a generalized complete intersection Calabi-Yau threefold.