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PreprintCC BY 4.0arXiv

Characterizing Contractions and Weighted Blowdowns

  • Soham Ghosh
  • Tyson Klingner
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Abstract

This paper gives a partial answer to a question of Dan Abramovich: consider a proper morphism f : 𝒳 β†’ 𝒡 with connected fibers, between smooth separated Deligne--Mumford stacks, which defines an isomorphism away from a smooth effective Cartier divisor β„° βŠ† 𝒳. Then, is f a weighted blowup? We confirm that f is an ordinary smooth blowup when 𝒳 and 𝒡 are smooth separated schemes of finite type over β„‚, and when f :𝒳 β†’ 𝒡 is a representable morphism of smooth separated Deligne--Mumford stacks. Further, we show that f is a weighted blowup when 𝒳 and 𝒡 are smooth separated Deligne--Mumford surfaces, i.e., dim 𝒳 = dim 𝒡 = 2. As an application we determine when a reduction morphism between Hassett moduli stacks of weighted stable curves is given by a blowup along a smooth center.

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Cite

BibTeXRIS
BibTeX
@misc{ghosh2026characterizing,
  title = {{Characterizing Contractions and Weighted Blowdowns}},
  author = {Soham Ghosh and Tyson Klingner},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04023},
  eprint = {2609.04023},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04023},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Characterizing Contractions and Weighted Blowdowns
AU  - Soham Ghosh
AU  - Tyson Klingner
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04023
UR  - https://arxiv.org/abs/2609.04023
AB  - This paper gives a partial answer to a question of Dan Abramovich: consider a proper morphism f : 𝒳 β†’ 𝒡 with connected fibers, between smooth separated Deligne--Mumford stacks, which defines an isomorphism away from a smooth effective Cartier divisor β„° βŠ† 𝒳. Then, is f a weighted blowup? We confirm that f is an ordinary smooth blowup when 𝒳 and 𝒡 are smooth separated schemes of finite type over β„‚, and when f :𝒳 β†’ 𝒡 is a representable morphism of smooth separated Deligne--Mumford stacks. Further, we show that f is a weighted blowup when 𝒳 and 𝒡 are smooth separated Deligne--Mumford surfaces, i.e., dim 𝒳 = dim 𝒡 = 2. As an application we determine when a reduction morphism between Hassett moduli stacks of weighted stable curves is given by a blowup along a smooth center.
ER  -