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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 317, Pages 179–197
DOI: https://doi.org/10.4213/tm4290 (Mi tm4290) 		 
Toric Varieties of Schröder Type

JiSun Huha, Seonjeong Parkb

a Department of Mathematics, Ajou University, 206 World cup-ro, Yeongtong-gu, Suwon, 16499, Korea
b Department of Mathematics Education, Jeonju University, 303 Cheonjam-ro, Wansan-gu, Jeonju, 55069, Korea
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DOI: https://doi.org/10.4213/tm4290
Abstract: A dissection of a polygon is obtained by drawing diagonals such that no two diagonals intersect in their interiors. In this paper, we define a toric variety of Schröder type as a smooth toric variety associated with a polygon dissection. Toric varieties of Schröder type are Fano generalized Bott manifolds, and they are isomorphic if and only if the associated Schröder trees are the same as unordered rooted trees. We describe the cohomology ring of a toric variety of Schröder type using the associated Schröder tree and discuss the cohomological rigidity problem.
Keywords: toric variety, polygon dissection, Schröder tree, generalized Bott manifold.
Funding agency Grant number
National Research Foundation of Korea NRF-2020R1A2C1A01011045
NRF-2021R1A6A1A10044950
Jeonju University
This work was supported by NRF-2020R1A2C1A01011045 and NRF-2021R1A6A1A10044950. This research was supported by the Research Grant of Jeonju University in 2021.
Received: April 1, 2022
Revised: June 6, 2022
Accepted: June 14, 2022
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 317, Pages 161–177
DOI: https://doi.org/10.1134/S0081543822020092
Bibliographic databases:
Document Type: Article
UDC: 512.7+519.17
MSC: Primary: 14M25, 57S12; Secondary: 05C60
Language: Russian
Citation: JiSun Huh, Seonjeong Park, “Toric Varieties of Schröder Type”, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Collected papers, Trudy Mat. Inst. Steklova, 317, Steklov Math. Inst., М., 2022, 179–197; Proc. Steklov Inst. Math., 317 (2022), 161–177
Citation in format AMSBIB
\Bibitem{HuhPar22}
\by JiSun~Huh, Seonjeong~Park
\paper Toric Varieties of Schr\"oder Type
\inbook Toric Topology, Group Actions, Geometry, and Combinatorics. Part~1
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 317
\pages 179--197
\publ Steklov Math. Inst.
\publaddr М.
\mathnet{http://mi.mathnet.ru/tm4290}
\crossref{https://doi.org/10.4213/tm4290}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538829}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 317
\pages 161--177
\crossref{https://doi.org/10.1134/S0081543822020092}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85141976689}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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