GSoC 2025 Meta Ticket: Classification of Maximal Exceptional Sequences on Smooth Fano Toric Varieties

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Description

This project extends SageMath’s functionality for studying maximal exceptional sequences on smooth Fano toric varieties. It introduces new examples from classification results, tools to detect acyclic line bundles, and automated construction of maximal-length exceptional collections. The module also supports mutation, normalization, and verification of fullness—that is, whether a sequence generates the derived category.

This is the meta ticket for the 2025 Google Summer of Code project Exceptional Collections on Fano Toric Varieties, tracking related issues and pull requests.

Mentor: @tscrim

Relevant Issues/PRs

• Introduce class FanoToricVariety_field for Gorenstein Fano Toric Varieties #40416 introduce the base class Gorenstein Fano toric variety for smooth Fano toric variety