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A Graded Domain Is Determined at Its Vertex. Applications to Invariant Theory

Conference paper
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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 319)

Abstract

We will prove that a positively graded domain/\(\mathbf{C}\) is uniquely determined by its completion at the irrelevant maximal ideal. As an application we will prove that the logarithmic Kodaira dimension of the smooth locus of a quotient of an affine space modulo a reductive algebraic group is \(-\infty \).

Keywords

Graded ring Logarithmic Kodaira dimension Invariant theory 

Mathematics Subject Classification (2000)

14L24 14L30 13A02 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology BombayMumbaiIndia

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