scholarly journals Geometric Invariant Theory

2017 ◽  
Author(s):  
Nolan R. Wallach
Keyword(s):  
Invariant Theory ◽  
Geometric Invariant Theory ◽  
Geometric Invariant

scholarly journals Tits Buildings and K-Stability

2019 ◽  
Vol 62 (3) ◽  
pp. 799-815 ◽  
Author(s):  
Giulio Codogni
Keyword(s):  
Continuous Function ◽  
Invariant Theory ◽  
Geometric Invariant Theory ◽  
Geometric Invariant ◽  
Test Configuration ◽  
Direct System ◽  
Cauchy Sequences

AbstractA polarized variety is K-stable if, for any test configuration, the Donaldson–Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct system of Tits buildings. We show that the Donaldson–Futaki invariant, conveniently normalized, is a continuous function on this space. We also introduce a pseudo-metric on the space of test configurations. Recall that K-stability can be enhanced by requiring that the Donaldson–Futaki invariant is positive on any admissible filtration of the co-ordinate ring. We show that admissible filtrations give rise to Cauchy sequences of test configurations with respect to the above mentioned pseudo-metric.

scholarly journals Autoequivalences of derived categories via geometric invariant theory

2016 ◽  
Vol 303 ◽  
pp. 1264-1299 ◽  
Author(s):  
Daniel Halpern-Leistner ◽  
Ian Shipman
Keyword(s):  
Invariant Theory ◽  
Derived Categories ◽  
Geometric Invariant Theory ◽  
Geometric Invariant
Sign in / Sign up

Export Citation Format

Share Document