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is unibranch. The notions of unibranch and geometrically unibranch points are used in some theorems in algebraic geometry. For example, there is the following result:
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there is a fundamental system of neighborhoods (in the classical topology) of
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is also a local ring. A unibranch local ring is said to be
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189:. Denote their function fields by
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117:of closed algebraic subsets of
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175:{\displaystyle f\colon X\to Y}
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267:{\displaystyle f^{-1}(y)}
52:(obtained by quotienting
492:Algebraic geometry stubs
125:whose intersection with
94:of the residue field of
311:Grothendieck, Alexandre
113:if for all complements
107:topologically unibranch
80:geometrically unibranch
431:-related article is a
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291:Zariski's main theorem
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228:{\displaystyle y\in Y}
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205:has separable degree
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101:. A complex variety
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429:commutative algebra
482:Algebraic geometry
372:algebraic geometry
337:10.1007/bf02684274
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134:normal ring
109:at a point
476:Categories
297:References
284:birational
105:is called
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33:local ring
248:−
220:∈
209:and that
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40:unibranch
18:Unibranch
317:(1961).
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140:Theorem
82:if the
56:by its
42:if the
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184:proper
427:This
370:This
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376:stub
203:K(X)
199:K(Y)
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193:and
191:K(X)
146:and
142:Let
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99:red
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96:A
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54:A
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36:A
20:)
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