Complex slices on a real variety Article Swipe
Let $X$ be a real algebraic variety with set of complex points $X_{\mathbb C}$ and set of real points $X_{\mathbb R}$. A complex slice of $X$ is a transverse intersection of $X_{\mathbb R}$ with a complex subvariety $V$ of $X_{\mathbb C}$. Complex slices are real algebraic varieties of a very special kind. They are cooriented, realize an integer cohomology class. A codimension 2 projective variety is a slice, iff it is a base of pencil of real algebraic hypersurfaces. We prove an upper bound for the linking number of a real projective curve bounding in its complexification with a slice of codimension two.
Related Topics
Concepts
Subvariety
Mathematics
Toric variety
Pencil (optics)
Variety (cybernetics)
Projective variety
Algebraic number
Codimension
Algebraic variety
Real algebraic geometry
Intersection (aeronautics)
Discrete mathematics
Set (abstract data type)
Base (topology)
Algebra over a field
Pure mathematics
Point (geometry)
Complex conjugate
Algebraic geometry
Affine variety
Function field of an algebraic variety
Disjoint sets
Combinatorics
Singular point of an algebraic variety
Dimension of an algebraic variety
Homogeneous coordinates
Bounding overwatch
Upper and lower bounds
Integer (computer science)
Real number
Piecewise
Metadata
- Type
- article
- Landing Page
- http://arxiv.org/abs/2511.19929
- https://arxiv.org/pdf/2511.19929
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7106862792
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W7106862792Canonical identifier for this work in OpenAlex
- Title
-
Complex slices on a real varietyWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
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2025-11-25Full publication date if available
- Authors
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Viro, OlegList of authors in order
- Landing page
-
https://arxiv.org/abs/2511.19929Publisher landing page
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https://arxiv.org/pdf/2511.19929Direct link to full text PDF
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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://arxiv.org/pdf/2511.19929Direct OA link when available
- Concepts
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Subvariety, Mathematics, Toric variety, Pencil (optics), Variety (cybernetics), Projective variety, Algebraic number, Codimension, Algebraic variety, Real algebraic geometry, Intersection (aeronautics), Discrete mathematics, Set (abstract data type), Base (topology), Algebra over a field, Pure mathematics, Point (geometry), Complex conjugate, Algebraic geometry, Affine variety, Function field of an algebraic variety, Disjoint sets, Combinatorics, Singular point of an algebraic variety, Dimension of an algebraic variety, Homogeneous coordinates, Bounding overwatch, Upper and lower bounds, Integer (computer science), Real number, PiecewiseTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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