Homepage of the project
"Complex contact manifolds and geometry of secants" (CoCoMaGeS)

Polish title:
Zespolone rozmaitości kontaktowe i geometria siecznych

The project was realized within the Sonata Bis (7th edition) programme of National Science Centre, Poland.


Time span of the project:

August 1st, 2018 -- July 31st, 2024 (60 months + 12 months of extension)

Project number:

2017/26/E/ST1/00231

Main Location:

Institute of Mathematics of Polish Academy of Sciences (IMPAN), Warsaw, Poland.

Participants:


Student scholarships:

The project has a possibility of funding several scholarships for students in the Master program and PhD program:

Postdoc positions:

Two postdoctoral positions are funded jointly with the Institute of Mathematics of the Polish Academy of Sciences. Contact manifolds are the main topic of the first position (awarded to Aleksandra Borówka). The deadline for applications for the first position was April 30th, 2018. Details and an official announcement are available here.
Secant varieties are the main topic of the second position (awarded to Francesco Galuppi). The deadline for applications for the second position was May 10th, 2021. Details and an official announcement are available here.

Articles that resulted from work supported by the grant:

    Preprints:

  1. "Cactus varieties of sufficiently ample embeddings of projective schemes have determinantal equations"
    Weronika Buczyńska, Jarosław Buczyński, Łucja Farnik
    arXiv:2412.00709

  2. "Cactus scheme, catalecticant minors, and scheme theoretic equations"
    Jarosław Buczyński, Hanieh Keneshlou
    arXiv:2410.21908

  3. "Rank and symmetries of signature tensors"
    Francesco Galuppi, Pierpaola Santarsiero
    arXiv:2407.20405

  4. "Invariant Monge-Ampere equations on contactified para-Kähler manifolds"
    Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
    arXiv:2402.08315

  5. "Geometry of first nonempty Terracini loci"
    Francesco Galuppi, Pierpaola Santarsiero, Douglas Torrance, Ettore Turatti
    arXiv:2311.09067

  6. "Characteristic polynomials and eigenvalues of tensors"
    Francesco Galuppi, Fulvio Gesmundo, Ettore Turatti, Lorenzo Venturello
    arXiv:2308.10957

  7. "Initial values of ML-degree polynomials"
    Maciej Gałązka
    arXiv:2212.12588

  8. Accepted for publication:

  9. "Third-order affine-invariant (systems of) PDEs in two independent variables as vanishing of the Fubini-Pick invariant"
    Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
    to appear in Rivista di Matematica della Universita di Parma, arXiv:2202.09894

  10. Published:

  11. "A note on dual abelian varieties"
    Aleksandra Borówka, Paweł Borówka
    Linear Algebra and its Applications, Volume 710, 1 April 2025, Pages 458-470 DOI: 10.1016/j.laa.2025.02.008 arXiv:2311.02718

  12. "Decomposing tensor spaces via path signatures"
    Carlos Amendola, Francesco Galuppi, Angel Rios, Pierpaola Santarsiero, Tim Seynnaeve
    Journal of Pure and Applied Algebra, Volume 229(1) (2025), pp. 1-19, DOI: 10.1016/j.jpaa.2024.107807, arXiv:2308.11571

  13. "Non-Defectivity of Segre-Veronese varieties"
    Hirotachi Abo, Maria Chiara Brambilla, Francesco Galuppi, Alessandro Oneto
    Proceedings of the American Mathematial Society (series B), Volume 11 (2024), pp. 589-602, DOI: 10.1090/bproc/248, arXiv:2406.20057

  14. "The moment map on the space of symplectic 3d Monge-Ampere equations"
    Jan Gutt, Gianni Manno, Giovanni Moreno, Robert Śmiech
    Adv. Differential Equations, 29(7/8) (2024), 575-654, DOI: 10.57262/ade029-0708-575, arXiv:2105.06675

  15. "Equations of tensor eigenschemes"
    Valentina Beorchia, Francesco Galuppi, Lorenzo Venturello
    Mathematics of Computations, Volume 93 (2024), pp. 589-602, DOI: 10.1090/mcom/3882, arXiv:2205.04413

  16. "Singular contact varieties"
    Robert Śmiech
    Manuscripta Mathematica, Volume 175 (2024), pp. 117-145, DOI: 10.1007/s00229-024-01561-3, arXiv:2212.07930

  17. "Projectively and affinely invariant PDEs on hypersurfaces"
    Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
    Proceedings of the Edinburgh Mathematical Society, Volume 67(3) (2024), pp. 714-739, DOI: 10.1017/S0013091524000233, arXiv:1907.06283

  18. "Toric Sarkisov links of toric Fano varieties"
    Gavin Brown, Jarosław Buczyński, Alexander Kasprzyk
    In: Cheltsov, I., Chen, X., Katzarkov, L., Park, J. (eds) Birational Geometry, Kähler-Einstein Metrics and Degenerations, pp 129-144 (2023) DOI: 10.1007/978-3-031-17859-7_6, arXiv:2207.08278

  19. "Distinguishing secant from cactus varieties"
    Maciej Gałązka, Tomasz Mańdziuk, Filip Rupniewski
    Foundations of Computational Mathematics, Volume 23 (2023), pp. 1167-1214, DOI: 10.1007/s10208-022-09566-8, arXiv:2007.16203

  20. "Generic identifiability of pairs of ternary forms"
    Valentina Beorchia, Francesco Galuppi
    Collectanea Mathematica, Volume 74 (2023), pp. 529-545, DOI: 10.1007/s13348-022-00363-8, arXiv:2106.13698

  21. "Spectral theory of weighted hypergraphs via tensors"
    Francesco Galuppi, Raffaella Mulas, Lorenzo Venturello
    Linear and Multilinear Algebra, Volume 71:3 (2023), pp. 317-347, DOI: 10.1080/03081087.2022.2030659, arXiv:2106.00277

  22. "On Rational Recursive Sequences"
    Lorenzo Clemente, Maria Donten-Bury, Filip Mazowiecki, Michał Pilipczuk
    40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023) Volume 254 (2023), pp. 24:1--24:21, DOI: 10.4230/LIPIcs.STACS.2023.24, arXiv:2210.01635

  23. "Secant non-defectivity via collisions of fat points"
    Francesco Galuppi, Alessandro Oneto
    Advances in Mathematics, 409 part B (2022), DOI: 10.1016/j.aim.2022.108657, arXiv:2104.02522

  24. "Algebraic torus actions on contact manifolds"
    Jarosław Buczyński, Jarosław A. Wiśniewski, with an appendix by Andrzej Weber
    J. Differential Geom. 121(2) (2022), pp. 227-289 DOI: 10.4310/jdg/1659987892, arXiv:1802.05002

  25. "Identifying limits of ideals of points in the case of projective space"
    Tomasz Mańdziuk
    Linear Algebra and its Applications Volume 634 (2022), pp. 149-178 DOI: 10.1016/j.laa.2021.11.003, arXiv:2011.14692

  26. "Apolarity, border rank and multigraded Hilbert scheme"
    Weronika Buczyńska, Jarosław Buczyński
    Duke Mathematical Journal, 2021, 170(16): 3659-3702, DOI: 10.1215/00127094-2021-0048, arXiv:1910.01944

  27. "Quaternion-Kähler manifolds near maximal fixed point sets of $S^1$-symmetries"
    Aleksandra Borówka
    Annali di Matematica Pura ed Applicata , Volume 2020, Issue 199, Pages 1243-1262, DOI: 10.1007/s10231-019-00920-2, arXiv:1904.08474

  28. "Singular curves of low degree and multifiltrations from osculating spaces"
    Jarosław Buczyński, Nathan Ilten, Emanuele Ventura
    International Mathematics Research Notices, Volume 2020, Issue 21, November 2020, Pages 8139-8182, DOI:10.1093/imrn/rnaa009, arXiv:1905.11860

Grant acknowledgements

The project support, even partial, should be explicitly acknowledged in all the publications, including theses, produced by postdocs and PhD/MSc students during the project. The acknowledgement should contain the keywords "National Science Centre, Poland" and the project number above, see the LaTeX templates below:

Related conferences and events

The following events are partially supported from the indirect costs of the grant: Other meetings related to the topics of the project and organised by team members: