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blowing up

in algebraic geometry, a transformation on an algebraic variety or scheme, wherein a closed subvariety is replaced with the space of lines passing through it (in the case of a point, a projective space), commonly used to resolve singularities
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blowing up

Summary

blowing up ranks in the top 2% of general entities by monthly Wikipedia readership (455 views/month).[1]

Key Facts

  • blowing up is a type of morphism of schemes[2].
  • blowing up is used for resolution of singularities[3].
  • blowing up's Stack Exchange tag is recorded as https://mathoverflow.net/tags/blow-ups[4].
  • blowing up's Stack Exchange tag is recorded as https://math.stackexchange.com/tags/blowup[5].
  • blowing up's maintained by WikiProject is recorded as WikiProject Mathematics[6].

Body

Definition and Type

blowing up is a type of morphism of schemes[2].

Use and Application

blowing up is used for resolution of singularities[3].

Why It Matters

blowing up ranks in the top 2% of general entities by monthly Wikipedia readership (455 views/month).[1] It has Wikipedia articles in 9 language editions, a strong signal of global cultural recognition.[7] It is known by 18 alternative names across languages and contexts.[8]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.

Aggregate / graph-position facts

  1. [1] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [7] ↑ . Wikidata sitelinks. wikidata.org.
  3. [8] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). blowing up. Retrieved April 10, 2026, from https://4ort.xyz/entity/blowing-up
MLA “blowing up.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/blowing-up.
BibTeX @misc{4ortxyz_blowing-up_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{blowing up}}, year = {2026}, url = {https://4ort.xyz/entity/blowing-up}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): blowing up — https://4ort.xyz/entity/blowing-up (retrieved 2026-04-10)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 5d ago · Twofivesixbot bot · 2026-05-26 view diff on Wikidata ↗
    Has use → resolution of singularities
    Aliases → —
    Subclass of → —
    Maintained by wikiproject → WikiProject Mathematics
    + 1 other property edited (see Wikidata diff for full list)
    "/* wbsetclaim-update-qualifiers:1||1|2 */ [[Property:P8189]]: 987007532039105171, mv to monolingual text names on J9U statements"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.