Most recent project: Algebraic varieties related to combinatorial structures
Polish National Science Centre project SONATA 2017/26/D/ST1/00755.
3 years: April 2018 - June 2021, extended until April 2023
Participants
Maria Donten-Bury (MIMUW) - principal investigator
Joachim Jelisiejew (IMPAN, MIMUW)
Maksymilian Grab (postdoc, MIMUW), July 2019 - June 2021
Topics
- Cox rings, in particular of resolutions of quotient singularities,
- computing GIT quotients for torus actions,
- varieties related to matrices and matrix groups, e.g. matrix Schubert varieties, Kazhdan-Lusztig varieties,
- varieties with torus actions (of low complexity), their polyhedral divisors and relation to deformation theory,
- tropicalization with additional structure.
Papers
- Joachim Jelisiejew and Łukasz Sienkiewicz, Białynicki-Birula decomposition for reductive groups
Journal de Mathématiques Pures et Appliquées 131: 290-325 (2019)
- Maria Donten-Bury, Paul Görlach and Milena Wrobel, Towards classifying toric degenerations of cubic surfaces
Le Matematiche (special issue on cubic surfaces) 75(2):537-557 (2020)
- Joachim Jelisiejew and Łukasz Sienkiewicz, Białynicki-Birula decomposition for reductive groups in positive characteristic
Journal de Mathématiques Pures et Appliquées 152: 189-210 (2021)
- Joachim Jelisiejew and Klemen Šivic, Components and singularities of Quot schemes and varieties of commuting matrices
Journal für die reine und angewandte Mathematik (Crelle's Journal), 2022(788): 129-187 (2022)
- Roser Homs, Joachim Jelisiejew, Mateusz Michałek and Tim Seynnaeve, Bounds on complexity of matrix multiplication away from CW tensors
Journal of Pure and Applied Algebra 226(12) (2022)
- Maria Donten-Bury, Laura Escobar and Irem Portakal, Complexity of the usual torus action on Kazhdan-Lusztig varieties
to appear in Algebraic Combinatorics (2023)
- Maria Donten-Bury, Laura Escobar and Irem Portakal, Moving blocks in diagrams and complexity of KL-varieties
in preparation (2023)
- Maria Donten-Bury, Cox rings and geometry of resolutions of 3-dimensional quotient singularities
in preparation (2023)
Previous projects
Cox rings of resolutions of quotient singularities
NCN 2012/07/N/ST1/03202 PRELUDIUM, 18 months: July 2013 - December 2014
Constructing algebraic varieties via finite group actions
MNiSW N N201 611240, 18 months: April 2011 - October 2012