Vladimir Lazić – Publications


  1. V. Lazić, Programming the Minimal Model Program: a proposal, Beitr. Algebra Geom. (2024), https://doi.org/10.1007/s13366-024-00742-1
  2. V. Lazić, Abundance for uniruled pairs which are not rationally connected, Enseign. Math. (2023), https://doi.org/10.4171/LEM/1065
  3. V. Lazić, S. Matsumura, Th. Peternell, N. Tsakanikas, Z. Xie, The Nonvanishing Problem for varieties with nef anticanonical bundle, Doc. Math. 28 (2023), no. 6, 1393–1440.
  4. V. Lazić, J. Moraga, N. Tsakanikas, Special termination for log canonical pairs, Asian J. Math. 27 (2023), no. 3, 423–440.
  5. V. Lazić, N. Tsakanikas, Special MMP for log canonical generalised pairs (with an appendix joint with Xiaowei Jiang), Selecta Math. New Ser. 28 (2022), no. 5, Paper No. 89
  6. V. Lazić, F.-O. Schreyer, Birational geometry and the canonical ring of a family of determinantal 3-folds, Rend. Istit. Mat. Univ. Trieste 54 (2022), Art. No. 9
  7. V. Lazić, N. Tsakanikas, On the existence of minimal models for log canonical pairs, Publ. Res. Inst. Math. Sci. 58 (2022), no. 2, 311–339.
  8. V. Lazić, F. Meng, On Nonvanishing for uniruled log canonical pairs, Electron. Res. Arch. 29 (2021), no. 5, 3297–3308.
  9. V. Lazić, K. Oguiso, Th. Peternell, Nef line bundles on Calabi-Yau threefolds, I, Int. Math. Res. Not. IMRN (2020), no. 19, 6070−6119.
  10. V. Lazić, Th. Peternell, Maps from K-trivial varieties and connectedness problems, Annales Henri Lebesgue 3 (2020), 473−500.
  11. V. Lazić, Th. Peternell, On Generalised Abundance, II, Peking Math. J. 3 (2020), no. 1, 1−46.
  12. V. Lazić, Th. Peternell, On Generalised Abundance, I, Publ. Res. Inst. Math. Sci. 56 (2020), no. 2, 353−389.
  13. E. Floris, V. Lazić, A travel guide to the canonical bundle formula, Birational Geometry and Moduli Spaces (E. Colombo, B. Fantechi, P. Frediani, D. Iacono, R. Pardini, eds.), Springer INdAM Series, vol. 39, Springer, 2020, pp. 37−55.
  14. E. Floris, V. Lazić, On the B-Semiampleness Conjecture, Épijournal Géom. Algébrique, Volume 3 (2019), Article Nr. 12
  15. V. Lazić, Th. Peternell, Abundance for varieties with many differential forms, Épijournal Géom. Algébrique, Volume 2 (2018), Article Nr. 1
  16. V. Lazić, K. Oguiso, Th. Peternell, The Morrison−Kawamata Cone Conjecture and Abundance on Ricci flat manifolds, Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau manifolds & Picard-Fuchs Equations (L. Ji, S.-T. Yau, eds.), Advanced Lectures in Mathematics, vol. 42, International Press, 2018, pp. 157−185.
  17. V. Lazić, K. Oguiso, Th. Peternell, Automorphisms of Calabi-Yau threefolds with Picard number three, Higher dimensional algebraic geometry in honour of Professor Yujiro Kawamata's sixtieth birthday, Adv. Stud. Pure Math., vol. 74, Mathematical Society of Japan, Tokyo, 2017, pp. 279−290.
  18. V. Lazić, Th. Peternell, Rationally connected varieties − on a conjecture of Mumford, Sci. China Math. 60 (2017), no. 6, 1019−1028. 
  19. A.-S. Kaloghiros, A. Küronya, V. Lazić, Finite generation and geography of models, Minimal Models and Extremal Rays (Kyoto 2011), Adv. Stud. Pure Math., vol. 70, Mathematical Society of Japan, Tokyo, 2016, pp. 215−245.
  20. T. Dorsch, V. Lazić, A note on the abundance conjecture, Algebr. Geom. 2 (2015), no. 4, 476−488.
  21. P. Cascini, V. Lazić, On the number of minimal models of a log smooth threefold, J. Math. Pures Appl. 102 (2014), 597−616.
  22. V. Lazić, Th. Peternell, On the Cone conjecture for Calabi-Yau manifolds with Picard number two, Math. Res. Lett. 20 (2013), no. 6, 1103−1113.
  23. V. Lazić, Around and beyond the canonical class, Birational Geometry, Rational Curves, and Arithmetic (F. Bogomolov, B. Hassett, Y. Tschinkel, eds.), Simons Symposia, Springer New York, 2013, pp. 171−203. 
  24. A. Corti, V. Lazić, New outlook on the Minimal Model Program, II, Math. Ann. 356 (2013), no. 2, 617−633.
  25. P. Cascini, V. Lazić, New outlook on the Minimal Model Program, I, Duke Math. J. 161 (2012), no. 12, 2415−2467.
  26. P. Cascini, V. Lazić, The Minimal Model Program revisited, Contributions to Algebraic Geometry (P. Pragacz, ed.), EMS Series of Congress Reports, EMS Publishing House, 2012, pp. 169−187.
  27. A. Corti, A.-S. Kaloghiros, V. Lazić, Introduction to the Minimal Model Program and the existence of flips, Bull. London Math. Soc. 43 (2011), no. 3, 415−448.


  1. V. Lazić, Metrics with minimal singularities and the Abundance conjecture, arXiv:2406.18233
  2. V. Lazić, Z. Xie, Rigid currents in birational geometry, arXiv:2402.05807
  3. V. Lazić, A few remarks on effectivity and good minimal models, arXiv:2401.14190
  4. V. Lazić, Z. Xie, Nakayama-Zariski decomposition and the termination of flips, arXiv:2305.01752
  5. V. Lazić, Adjoint rings are finitely generated, arXiv:0905.2707 (supersedes arXiv:0707.4414 and arXiv:0812.3046; a simplified proof published in Duke Math. J. 161 (2012))
  6. V. Lazić, Towards finite generation of the canonical ring without the MMP, arXiv:0812.3046
  7. V. Lazić, On Shokurov-type b-divisorial algebras of higher rank, arXiv:0707.4414


Fachrichtung Mathematik
Campus, Gebäude E2 4
Universität des Saarlandes
66123 Saarbrücken