A Perfectoid Framework for Moduli of Log Fano Varieties Article Swipe
Revista, Zen
,
MATH, 10
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17834928
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17834928
This paper develops a novel perfectoid framework for the study of moduli spaces of log Fano varieties. Log Fano varieties, characterized by their anti-canonical divisor being ample relative to a boundary, play a crucial role in birational geometry and the Minimal Model Program. However, the construction of their moduli spaces, particularly those allowing for mild singularities, presents significant challenges. We propose leveraging the powerful machinery of perfectoid spaces, introduced by Scholze, to address these issues. By working in a mixed characteristic setting, perfectoid spaces offer a unique perspective on p-adic geometry and provide tools like the tilting equivalence that allow for a deeper understanding of algebraic varieties. This framework aims to establish a robust theory for defining and constructing moduli stacks of log Fano varieties over perfectoid rings, enabling the exploration of their geometric properties across different characteristics. We discuss the definition of perfectoid families of log Fano varieties, criteria for boundedness and properness in this context, and outline potential applications to the classification and study of these important geometric objects. The methodology hinges on extending notions of stability and deformation theory to the perfectoid setting, paving the way for new insights into the arithmetic and geometric structure of log Fano moduli.
Related Topics
Concepts
Fano plane
Moduli space
Mathematics
Moduli
Equivalence (formal languages)
Algebraic geometry
Pure mathematics
Divisor (algebraic geometry)
Algebraic number
Stability (learning theory)
Deformation theory
Algebra over a field
Geometry
Discrete mathematics
Geometric invariant theory
Algebraic structure
Perspective (graphical)
Birational geometry
Current (fluid)
Wedge (geometry)
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17834928
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7108896677
All OpenAlex metadata
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https://openalex.org/W7108896677Canonical identifier for this work in OpenAlex
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https://doi.org/10.5281/zenodo.17834928Digital Object Identifier
- Title
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A Perfectoid Framework for Moduli of Log Fano VarietiesWork title
- Type
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articleOpenAlex work type
- Publication year
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2025Year of publication
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2025-12-06Full publication date if available
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Revista, Zen, MATH, 10List of authors in order
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https://doi.org/10.5281/zenodo.17834928Publisher landing page
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://doi.org/10.5281/zenodo.17834928Direct OA link when available
- Concepts
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Fano plane, Moduli space, Mathematics, Moduli, Equivalence (formal languages), Algebraic geometry, Pure mathematics, Divisor (algebraic geometry), Algebraic number, Stability (learning theory), Deformation theory, Algebra over a field, Geometry, Discrete mathematics, Geometric invariant theory, Algebraic structure, Perspective (graphical), Birational geometry, Current (fluid), Wedge (geometry)Top concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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