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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2025, Volume 329, Pages 132–164
DOI: https://doi.org/10.4213/tm4465 (Mi tm4465) 		 
$G$-Coregularity of del Pezzo Surfaces

K. V. Loginovabc, V. V. Przyjalkowskiab , A. S. Trepalinab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
c Laboratory of Algebraic Geometry and Homological Algebra, Moscow Institute of Physics and Technology, Dolgoprudny, Moscow oblast, Russia
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DOI: https://doi.org/10.4213/tm4465
Abstract: We introduce and study the notion of $G$-coregularity of algebraic varieties endowed with an action of a finite group $G$. We compute the $G$-coregularity of smooth del Pezzo surfaces of degree at least $6$, and give a characterization of groups that can act on conic bundles with $G$-coregularity $0$. We describe the relations between the notions of $G$-coregularity, $G$-log canonical thresholds, $G$-birational rigidity, and exceptional quotient singularities.
Keywords: Fano variety, coregularity, complements, dual complex.
Funding agency Grant number
National Research University Higher School of Economics
The article was prepared within the framework of the project “International Academic Cooperation” at HSE University.
Received: January 30, 2025
Revised: April 21, 2025
Accepted: June 5, 2025
Published: 03.09.2025
English version:
Proceedings of the Steklov Institute of Mathematics, 2025, Volume 329, Pages 117–147
DOI: https://doi.org/10.1134/S0081543825600723
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: K. V. Loginov, V. V. Przyjalkowski, A. S. Trepalin, “$G$-Coregularity of del Pezzo Surfaces”, Birational Geometry and Fano Varieties, Collected papers. Dedicated to Yuri Gennadievich Prokhorov on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 329, Steklov Math. Inst., Moscow, 2025, 132–164; Proc. Steklov Inst. Math., 329 (2025), 117–147
Citation in format AMSBIB
\Bibitem{LogPrzTre25}
\by K.~V.~Loginov, V.~V.~Przyjalkowski, A.~S.~Trepalin
\paper $G$-Coregularity of del Pezzo Surfaces
\inbook Birational Geometry and Fano Varieties
\bookinfo Collected papers. Dedicated to Yuri Gennadievich Prokhorov on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2025
\vol 329
\pages 132--164
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4465}
\crossref{https://doi.org/10.4213/tm4465}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2025
\vol 329
\pages 117--147
\crossref{https://doi.org/10.1134/S0081543825600723}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105017139274}
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