Mathematisches Institut
Ernst-Abbe-Platz 2
Friedrich-Schiller-Universität Jena
andriyregeta@gmail.com

Publications

1. Automorphisms of the Lie algebra of vector fields on affine n-Space (with H. Kraft), J. Eur. Math. Soc, Vol.

    19, Issue 5, 2017,  pp. 1577-1588.

2. Is the affine space determined by its automorphism group? (with H. Kraft and I. van Santen), Int. Math. Res. Not.,

     Vol. 2021, Issue 6,  pp. 4280–4300.

3.  Characterizing quasi-affine spherical varieties via the automorphism group (with I. van Santen), Journal de

      l’École polytechnique — Mathématiques, Vol. 8 (2021) pp. 379-414.

4. Bracket width of simple Lie algebras (with A. Dubouloz and B. Kunyavskii), Doc. Math. 26, 1601-1627 (2021).

    (B. Kunyavskii gave a recorded talk on this research work at the conference "Affine Algebraic Groups, Motives

    and Cohomological Invariants" in Banff.)

5. On the characterization of Danielewski surfaces by their automorphism group (with A. Liendo and C. Urech),

     Transform. Groups, Vol. 25, No. 4, 2022.

6. Vector Fields and Automorphism Groups of Danielewski Surfaces (with M. Leuenberger), Int. Math. Res. Not., Vol.

     2022, Issue 6, pp. 4720–4752.

7. Characterisation of  n-dimensional  normal affine SL_n-varieties, Transform. Groups, Vol. 27, pp. 271–293 (2022).

8. When is the automorphism group of an affine variety nested?  (with A. Perepechko), Transf. Groups, Vol. 28, pp.

    401-412 (2023). (Sasha gave a recorded talk on an this work at the  conference  Algebraic Geometry - Mariusz

     Koras in memoriam").

9. Characterisation of affine surfaces by their automorphism groups (with A. Liendo and C. Urech)  arXiv:1805.03991

     to appear in Ann. Sc. Norm. Super. di Pisa, doi:10.2422/2036-2145.201905_009

     (C. Urech  gave a recorded talk on an this work at the conference "Algebraic Geometry - Mariusz Koras 

     in  memoriam").

10. Families of commuting automorphisms, and a characterization of the affine space (with S. Cantat and  J. Xie),  

      American Journal of Mathematics 145, no. 2 (2023): 413-434.  muse.jhu.edu/article/885815.

11. Bracket width of the Lie algebra of vector fields on a smooth affine curve (with I. Makedonskyi), 

     Journal of Lie Theory 33 (2023), No. 3, 919--923.

12. Small G-varieties (with H. Kraft and S. Zimmermann), Canad. J.  of Math., doi:10.4153/S0008414X22000682  

       (H. Kraft gave a recorded talk on this work at the "Quadratic forms, Linear algebraic groups and Beyond" Online

       Seminar).     

13. Lie subalgebras of vector fields on affine 2-space and the Jacobian conjecture, to appear in Ann. Inst. Fourier.

14. Automorphism groups of affine varieties   without non-algebraic elements (with A. Perepechko)   

      arXiv:2203.08950   to appear in Proc. Amer. Math. Soc.

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Preprints

15. Characterizing Affine Toric varieties via the automorphism group (with I. van  Santen) arXiv:2112.04784        

       (submitted). (I gave a recorded talk on this work at the "Seminar on Algebraic Transformation Groups".)

16. Characterization of affine G_m-surfaces of hyperbolic type, arXiv:2202.10761 (submitted).

17. On the annihilators of rational functions in the Lie algebra of derivations of  K[x,y] (with O. Iena and 

       A. Petravchuk)  arXiv:0910.4465

18. When is the automorphism group of an affine variety  linear? (submitted).

19. On the characterization of affine toric varieties by their automorphism group (with R. Díaz

      and A. Liendo)  arXiv:2308.08040 (submitted).