Algebraic Geometry: Varieties and Structures

Research topics Varieties with group actions, via nef tangent bundle Varieties with nef tangent bundle in positive characteristic Varieties with group actions, via generalized jet bundles Resolutions of symplectic singularities Hyper-Kaehler manifolds Complex contact manifolds Fano spaces Derived category of coherent sheaves over Mori Dream Space Algebraic structures in physics and biology

The team

• Weronika Buczynska
• Jaroslaw Buczynski
• Maria Donten-Bury (Oct. 2014 - Sep. 2017)
• Maciej Galazka (Oct.2016 - Sep. 2018)
• Robin Guilbot (Sep. 2015 - Aug. 2018)
• Oskar Kedzierski
• Adrian Langer (PI)
• Tomasz Mandziuk (Oct. 2017 - Sep. 2018)
• Mateusz Michalek
• Abdo Roig-Maranges (Sep. 2016 - Aug. 2017)
• Eleonora Romano (Sep. 2017 - Aug 2018.)
• Lukasz Sienkiewicz (Oct. 2015 - Sep. 2018)
• Luis Eduardo Sola Conde
• Andrzej Weber
• Jaroslaw Wisniewski (PI)
• Magdalena Zielenkiewicz (Oct. 2015 - May 2016)

Activities related to the project

• September Algebraic Geometry Schools
• Activities in 2019:
  • September School in Algebraic Geometry: Homogeneous Spaces, Characteristic Classes, September 2019.
• Activities in 2018:
  • Mariusz Koras in memoriam, May 2018.
  • Varieties: Arithmetics and Transformations, Simons semester, September-November 2018.
• Activities in 2017:
  September school in Lukecin: Binomial Ideals, September 2017.
• Activities in 2016:
  • Mini-semester at Banach Center, April-June 2016.
  • Varieties of Calabi-Yau type (K3, Hyperkaehler, Calabi-Yau), April 2016.
  • Varieties with trivial canonical bundles, June 2016.
• Activities in 2015:
  • CIRM workshop in Levico: Hyper-Kaehler Manifolds and Related Structures in Algebraic and Differential Geometry, November 2015.
  • September school in Lukecin: Cox Rings and Mori Dream Spaces, September 2015.
  • Algebraic Geometry, Warsaw 1960-2015, March 2015.
• Activities in 2014:
  • September school in Lukecin: Topics in characteristic p>0 and p-adic geometry , September 2014.
  • Spring schools in Mainz: Contact geometry and rational curcves, March 2014.

Publications

1. Michela Artebani, Paola Comparin, Robin Guilbot, Families of Calabi-Yau hypersurfaces in Q-Fano toric varieties, Journal de Mathematiques Pures et Appliquees (2016).
2. Michela Artebani, Paola Comparin, Robin Guilbot, Quasismoooth hypersurfaces in toric varieties, Proceedings AMS (2019).
3. Weronika Buczynska, Jaroslaw Buczynski, Apolarity, border rank and multigraded Hilbert scheme
4. Weronika Buczynska, Jaroslaw Buczynski, Mateusz Michalek, Hackbusch Conjecture on tensor formats, Journal de Mathematiques Pures et Appliquees (2015).
5. Jaroslaw Buczynski, Giovanni Moreno, Complex contact manifolds, varieties of minimal rational tangents, and exterior differential systems, Banach Center Publ. 117 (2019).
6. Jaroslaw Buczynski, Elisa Postinghel, Filip Rupniewski, On Strassen's rank additivity for small three-way tensors, SIAM J. Matrix Analysis Appl., to appear.
7. Jaroslaw Buczynski, Jaroslaw Wisniewski, Andrzej Weber, Algebraic torus actions on contact manifolds, J. Diff. Geom, to appear.
8. Laura Colmenarejo, Francesco Galuppi, Mateusz Michalek Toric geometry of path signature varieties
9. Adam Czaplinski, Mateusz Michalek, Tim Seynnaeve, Uniform matrix product states from an algebraic geometer's point of view
10. Maria Donten-Bury, Bert van Geemen, Grzegorz Kapustka, Michal Kapustka, Jaroslaw Wisniewski, A very special EPW sextic and two IHS fourfolds, Geometry and Topology (2017).
11. Maria Donten-Bury, Andrzej Weber, Equivariant Hirzebruch classes and Molien series of quotient singularities, Transformation Groups, (2017).
12. Maria Donten-Bury, Jaroslaw Wisniewski, On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32, Kyoto Journal of Mathematics (2017).
13. Laszlo Feher, Richard Rimanyi, Andrzej Weber, Characteristic classes of orbit stratification, the axiomatic approach, Springer Proceedings in Mathematics & Statistics, to appear.
14. Joseph Gubeladze, Mateusz Michalek, The poset of rational cones, Pacific Journal of Mathematics (2018).
15. Corey Harris, Mateusz Michalek, Emre Can Sertoz, Computing images of polynomial maps, Advances in Computational Mathematics (2019)
16. Akihiro Higashitani, Mario Kummer, Mateusz Michalek, Interlacing Ehrhart polynomials of reflexive polytopes, Selecta Mathematica (2018)
17. Joachim Jelisiejew, Lukasz Sienkiewicz, Bialynicki-Birula decomposition for reductive groups, Journal de Mathematiques Pures et Appliquees (2019).
18. Adrian Langer, Generic positivity and foliations in positive characteristic, Advances in Mathematics (2015).
19. Adrian Langer, The Bogomolov-Miyaoka-Yau inequality for logarithmic surfaces in positive characteristic, Duke Mathematical Journal (2016).
20. Adrian Langer, Birational geometry of compactifications of Drinfeld half-spaces over a finite field, Advances in Mathematics (2019)
21. Adrian Langer, Nearby cycles and semipositivity in positive characteristic,
22. Tomasz Mandziuk, Cox rings and algebraic maps, Mathematische Nachrichten (2019)
23. Mateusz Michalek, Book review: Geometry and complexity theory by J.M. Landsberg, Bull. AMS.
24. Mateusz Michalek, Bernd Sturmfels, Caroline Uhler, Piotr Zwiernik, Exponential varieties, Proceedings of London Mathematical Society (2016).
25. Mateusz Michalek, Yaroslav Shitov, Quantum version of Wielandt's Inequality revisited, IEEE Transactions Inf. Theory (2019).
26. Mateusz Michalek, Tim Seynnaeve, Frank Verstraete, A tensor version of the quantum Wielandt theorem, SIAM J. Matrix Analysis Appl. (2019)
27. Malgorzata Mikosz, Andrzej Weber, Equivariant Hirzebruch class for quadratic cones via degenerations, Journal of Singularities (2015).
28. Malgorzata Mikosz, Andrzej Weber, Triality, characteristic classes, D4 and G2 singularities, Journal of homotopy and related structures (2014).
29. Malgorzata Mikosz, Andrzej Weber, Elliptic classes, McKay correspondence,and theta identities, J. Alg. Combinatorics, to appear.
30. Pedro Montero, Eleonora Anna Romano, A characterization of some Fano 4-folds through conic fibrations, International Mathematics Research Notices (2019).
31. Roberto Munoz, Gianluca Occhetta, Luis E. Sola Conde, , Nestings of rational homogeneous varieties , Transformation Groups , to appear.
32. Roberto Munoz, Gianluca Occhetta, Luis E. Sola Conde, Kiwamu Watanabe, Jaroslaw Wisniewski, A survey on the Campana-Peternell Conjecture, Rendiconti dell'Instituto di Matematica dell'Universita di Trieste (2015).
33. Gianluca Occhetta, Eleonora Anna Romano, Luis E. Sola Conde, Jaroslaw Wisniewski, Small bandwidth C* actions and birational geometry
34. Gianluca Occhetta, Luis E. Sola Conde, Deformation of Bott-Samelson varieties and variations of isotropy structures, J. Pure Appl. Algeba, to appear.
35. Gianluca Occhetta, Luis E. Sola Conde, Kiwamu Watanabe, Jaroslaw Wisniewski, Fano manifolds whose elementary contractions are smooth P^1-fibrations, Annali della Scuola Normale di Pisa - Classe di Scienze (2017).
36. Gianluca Occhetta, Luis E. Sola Conde, Jaroslaw Wisniewski, Flag bundles on Fano manifolds, Journal de Mathematiques Pures et Appliquees (2016).
37. Andrzej Weber Hirzebruch class and Bialynicki-Birula decomposition, Transformation Groups (2017).
38. Yang Qi, Mateusz Michalek, Lek-Heng Lim, Complex best r-term approximations almost always exist in finite dimensions, Applied and Computational Harmonic Analysis (2019)
39. Richard Rimanyi, Andrzej Weber, Elliptic classes of Schubert cells via Bott-Samelson resolution
40. Eleonora Anna Romano, On some Fano 4-folds with Lefschetz defect 3
41. Eleonora Anna Romano, Jaroslaw Wisniewski, Adjunction for varieties with C* action
42. Andrzej Weber, Equivariant Hirzebruch class for singular varieties, Selecta Matematica (2016).
43. Andrzej Weber, Leray spectral sequence for complements of certain arrangements of smooth submanifolds, in INDAM conference proceedings (2016).
44. Andrzej Weber, Jaroslaw Wisniewski, On rigidity of flag varieties, International Mathematics Research Notices (2018).
45. Andrzej Weber, Magdalena Zielenkiewicz, Residues formulas for the push-forward in K-theory, the case of G2/P, Journal of Algebraic Combinatorics (2018)