Martin Kalck

Publications and Preprints

  1. Length of triangulated categories,
    with Y. Hirano and G. Ouchi, arXiv:2404.07583v2 (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,
    arXiv:2401.08378, (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,
    arXiv:2006.09733, (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.