/-
Copyright (c) 2026 OpenAI. All rights reserved.
Released under Apache 2.0 license.
Authors: OpenAI
-/
import OAI.AlgebraicGeometry.CartierSections.ChartCompactness
import OAI.AlgebraicGeometry.CartierSections.RetractionBounds
import OAI.AlgebraicGeometry.CartierSections.LocalMultiplier

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# Local algebra of monomial retractions

Local results for *Uniform Cartier sections for Fano-type contractions*, Section E:
algebraic-series degree bounds and isolated jets, formal coordinates in closed étale
charts, monomial valuations and their extensions to fraction fields, and compactness
of normalized cones in the topology of pointwise evaluation. The local multiplier
algebra describes principal ideal sums and the convex regions defined by rounded
divisor coefficients.
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