Martin Kalck

Publications and Preprints

  1. Length of triangulated categories, with Y. Hirano and G. Ouchi,
    Advances in Mathematics, Volume 483, Article ID 110660, 40 p. (2025). (pdf).


  2. Dimension formulas for period spaces via motives and species,with A. Huber,
    arXiv:2405.21053, (pdf).


  3. Obstructions to semiorthogonal decompositions for singular projective varieties II: Representation theory,
    with C. Klapproth and N. Pavic, arXiv:2404.07816, (pdf).


  4. Cluster categories for completed infinity-gons I: Categorifying triangulations, with İ. Çanakçı and M. Pressland,
    to appear Journal of the LMS, (pdf); see also OWR 02/2024 for a summary.


  5. A finite dimensional algebra with a phantom (a corollary of an example by J. Krah),
    arXiv:2304.08417, (pdf).


  6. Classifying dg-categories of matrix factorizations,
    arXiv:2108.03292, (pdf).


  7. A new equivalence between singularity categories of commutative algebras,
    Advances in Mathematics, Volume 390 (2021), 107913, (pdf).


  8. Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory, with N. Pavic and E. Shinder,
    Moscow Mathematical Journal, vol. 21, issue 3, 567--592 (2021), (pdf).


  9. Relative singularity categories III: Cluster resolutions, with D. Yang,
    Mathematische Zeitschrift, Volume 311, No. 2, Paper No. 39, 19 p. (2025). (pdf).


  10. Relative singularity categories II: dg-models, with D. Yang,
    arXiv:1803.08192, (pdf).


  11. Ringel duality for certain strongly quasi-hereditary algebras, with J. Karmazyn,
    European Journal of Mathematics 4 (2018), 1100--1140,
    Special volume dedicated to the memory of William Edge, (pdf).


  12. Noncommutative Knörrer type equivalences via noncommutative resolutions of singularities, with J. Karmazyn,
    arXiv:1707.02836, (pdf).


  13. Derived categories of graded gentle one-cycle algebras, with D. Yang,
    Journal of Pure and Applied Algebra, Volume 222, Issue 10, (2018), 3005--3035, (pdf).


  14. Derived categories of quasi-hereditary algebras and their derived composition series,
    In Representation theory - current trends and perspectives, EMS Ser. Congr. Rep., 269--308. Eur. Math. Soc., Zürich, 2017, (pdf).


  15. Spherical subcategories in representation theory, with A. Hochenegger and D. Ploog,
    Mathematische Zeitschrift 291 (1-2): 113--147, 2019, (pdf).


  16. Frobenius categories, Gorenstein algebras and rational surface singularities,
    with O. Iyama, M. Wemyss and D. Yang,
    Compositio Mathematica, vol. 151, issue 03, 502--534 (2015), (pdf).


  17. Spherical subcategories in algebraic geometry, with A. Hochenegger and D. Ploog,
    Mathematische Nachrichten, 289 (2016) 1450--1465, (pdf).


  18. Singularity categories of gentle algebras,
    Bulletin of the London Mathematical Society 47 (2015) 65--74, (pdf).


  19. Relative singularity categories I: Auslander resolutions, with D. Yang,
    Advances in Mathematics, vol. 301, 973--1021 (2016), (pdf).


  20. The relative singularity category of a non-commutative resolution of singularities, with I. Burban,
    Advances in Mathematics, vol. 231, no. 1, 414--435 (2012), (pdf).



Conference Proceedings:

    Derived categories of singular varieties and finite dimensional algebras,
    in Oberwolfach Report 07/2023, Representation Theory of Quivers and Finite-Dimensional Algebras (pdf).
    (Based on upcoming joint works with Y.Kawamata & N.Pavic and C. Klapproth & N. Pavic)

    On equivalences between singularity categories of commutative rings,
    in Oberwolfach Report 06/2023, Resolutions in Local Algebra and Singularity Theory (pdf).
    (Based on articles 14. and 15. above.)

    On Leclerc's Frobenius categories,
    In proceedings of the CRM-workshop Homological Bonds between Commutative Algebra and Representation Theory
    in Research Perspectives CRM Barcelona , Spring 2015, vol. 5, Trends in Mathematics, Springer-Birkhäuser, (pdf).

    Relative singularity categories,
    in Oberwolfach Report 44/2013, Matrix Factorizations in Algebra, Geometry, and Physics (pdf).
    (Based on articles 2. and 5. above.)


Theses:

    Relative singularity categories, PhD Thesis, Bonn 2013, (pdf).

    Verallgemeinerungen präprojektiver Algebren, Diploma Thesis (in German), Bonn 2009.