Algebraic quotients and Geometric Invariant Theory

Descent of Coherent Sheaves and Complexes to Geometric Invariant Theory Quotients

Fix a quasi-projective scheme X over a field of characteristic zero that is equipped with an action of a reductive algebraic group G. Fix a polarization H of X that linearizes the G-action. We give necessary and sufficient conditions for a G-equivariant coherent sheaf on X to descend to the GIT quotient X/G, or for a bounded-above complex of G-equivariant coherent sheaves on X to be G-equivaria...

Descent of Coherent Sheaves and Complexes to Geometric Invariant Theory Quotients: Draft

Fix a quasi-projective scheme X over a field of characteristic zero that is equipped with an action of a reductive algebraic group G. Fix a polarization H of X that linearizes the G-action. We give necessary and sufficient conditions for a G-equivariant coherent sheaf on X to descend to the GIT quotient X/G, or for a bounded-above complex of G-equivariant coherent sheaves on X to be G-equivaria...

Basic geometric invariant theory

Algebraic Geometric Coding Theory

Acknowledgements Firstly, I would like to thank my supervisor, Dr David R. Kohel whose many helpful comments and patient guidance made this thesis possible. Secondly, I would like to thank David Gruenwald for volunteering his time to proofread this thesis. Almost all of his recommendations were taken on board. This thesis is the better for it. To a less extent, my thanks go to the IT school of ...

Geometric invariant theory and flips

Ever since the invention of geometric invariant theory, it has been understood that the quotient it constructs is not entirely canonical, but depends on a choice: the choice of a linearization of the group action. However, the founders of the subject never made a systematic study of this dependence. In light of its fundamental and elementary nature, this is a rather surprising gap, and this pap...