Invariant_Theory

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title: Invariant Theory permalink: wiki/Invariant_Theory/ layout: wiki

To do for Kstability package

• write methods for computing Futaki and Chow invariants
• write documentation and tests
• write method for computing extremal vector field. needs to find holomorphic vector fields on projective variety.

To do for AbelianTautologicalRings package

• Write the skeleton of the AbelianTautologicalRings package (done, Aug 5)
• Implement auxiliary functions for working with monomials (done, Aug 6)
• Implement Polishchuk differential operator for Jacobians (done, Aug 6)
• Implement iterations of Polishchuk differential operator for Jacobians (done, Aug 7)
• Implement generation of the ideal of relations for Jacobians (done, Aug 8)
• Implement auxiliary differential operators for tautological cycles on Jacobians (done, Aug 9)
• Implement Fourier transform for tautological cycles on Jacobians (done, Aug 9)
• Add an option to modelRing and abelianTautologicalRing methods to make a choice of the name for the indexed variable (done, Aug 23)
• Document the option in modelRing and abelianTautologicalRing methods to make a choice of the name for the indexed variable (done, Aug 23)
• In abelianTautologicalRing method check if the model ring for the given g has already been created. If yes, use it, else create it

Invariants package

• Wrote code for derksen's algorithm (need to change tensor products to towers of rings for better elimination)
• Need to (understand how to) implement reynolds operators

EquivariantResolutions package

• Need to complete documentation
• Need to add examples
• Need to add functions to decompose to highest weight modules
• Add weights of graded components of (quotient) rings