Funded projects

Between September 2013 and September 2020, Vladimir Lazić's Emmy Noether Group Gute Strukturen in der höherdimensionalen birationalen Geometrie was funded by the Deutsche Forschungsgemeinschaft.

Members

Publications

1. V. Lazić, J. Moraga, N. Tsakanikas, Special termination for log canonical pairs, arXiv:2007.06458
2. V. Lazić, F.-O. Schreyer, Birational geometry and the canonical ring of a family of determinantal 3-folds, arXiv:1911.10954
3. V. Lazić, Abundance for uniruled pairs which are not rationally connected, arXiv:1908.06945
4. V. Lazić, F. Meng, On Nonvanishing for uniruled log canonical pairs, Electron. Res. Arch. 29 (2021), no. 5, 3297­­­–3308, arXiv:1907.11991
5. 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, arXiv:1907.10490
6. V. Lazić, N. Tsakanikas, On the existence of minimal models for log canonical pairs, to appear in Publ. Res. Inst. Math. Sci., arXiv:1905.05576
7. V. Lazić, Th. Peternell, On Generalised Abundance, II, Peking Math. J. 3 (2020), no. 1, 1−46, arXiv:1809.02500
8. V. Lazić, Th. Peternell, Maps from K-trivial varieties and connectedness problems, Annales Henri Lebesgue 3 (2020), 473−500, arXiv:1808.01115
9. E. Floris, V. Lazić, On the B-Semiampleness Conjecture, Épijournal Géom. Algébrique, Volume 3 (2019), Article Nr. 12, arXiv:1808.00717
10. V. Lazić, Th. Peternell, On Generalised Abundance, I, Publ. Res. Inst. Math. Sci. 56 (2020), no. 2, 353−389, arXiv:1808.00438
11. 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 (Lizhen Ji, Shing-Tung Yau, eds.), Advanced Lectures in Mathematics, vol. 42, International Press, 2018, pp. 157−185, arXiv:1611.00556
12. D. Martinelli, S. Schreieder, L. Tasin, On the number and boundedness of minimal models of general type, Ann. Sci. Éc. Norm. Supér. (4) 53 (2020), no. 5, 1183-1210, arXiv:1610.08932
13. V. Lazić, Th. Peternell, Rationally connected varieties − on a conjecture of Mumford, Sci. China Math. 60 (2017), no. 6, 1019−1028, arXiv:1608.04706
14. S. Schreieder, L. Tasin, Kähler structures on spin 6-manifolds, Math. Ann. 373 (2019), 397−419, arXiv:1606.09237
15. V. Lazić, Th. Peternell, Abundance for varieties with many differential forms, Épijournal Géom. Algébrique, Volume 2 (2018), Article Nr. 1, arXiv:1601.01602
16. V. Lazić, K. Oguiso, Th. Peternell, Nef line bundles on Calabi-Yau threefolds, I, Int. Math. Res. Not. IMRN, Vol. 2020, No. 19, 6070−6119, arXiv:1601.01273
17. C. Bisi, P. Cascini, L. Tasin, A remark on the Ueno-Campana's threefold, Michigan Math. J. 65 (2016), no. 3, 567−572, arXiv:1512.06639
18. S. Schreieder, L. Tasin, Algebraic structures with unbounded Chern numbers, J. Topol. 9 (2016), 849−860, arXiv:1505.03086
19. P. Cascini, L. Tasin, On the Chern numbers of a smooth threefold, Trans. Amer. Math. Soc. 370 (2018), no. 11, 7923–7958, arXiv:1412.1686
20. T. Dorsch, V. Lazić, A note on the abundance conjecture, Algebraic Geometry 2 (2015), no. 4, 476−488, arXiv:1406.6554
21. 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, arXiv:1310.8151

Between July 2015 and March 2017 Vladimir Lazić was a Principal Investigator (together with Daniel Greb and Daniel Huybrechts) in the Subproject M08-9 Birational geometry of hyperkähler manifolds of the SFB/TR 45 Periods, moduli spaces and arithmetic of algebraic varieties funded by the Deutsche Forschungsgemeinschaft.

Since January 2021 Vladimir Lazić is a Principal Investigator (together with Frank-Olaf Schreyer and Ulrich Thiel) in the Project A23 Conjectures and new examples in birational geometry of the SFB/TRR 195 Symbolic Tools in Mathematics and their Application funded by the Deutsche Forschungsgemeinschaft.

Postdocs

Publications

1. V. Lazić,  Z. Xie, Rigid currents in birational geometry, arXiv:2402.05807
2. V. Lazić, A few remarks on effectivity and good minimal models, to appear in Pure Appl. Math. Q., arXiv:2401.14190
3. V. Lazić, Programming the Minimal Model Program: a proposal, Beitr. Algebra Geom. (2024), https://doi.org/10.1007/s13366-024-00742-1, arXiv:2310.01097
4. J. Schmitt, The class group of a minimal model of a quotient singularity, arXiv:2309.05402
5. V. Lazić, Z. Xie, Nakayama-Zariski decomposition and the termination of flips, arXiv:2305.01752
6. I. Stenger, Z. Xie, Cones of divisors on P³ blown up at eight very general points, arXiv:2303.12005
7. D. Eisenbud, F.-O. Schreyer, Hyperelliptic curves and Ulrich sheaves on the complete intersection of two quadrics, arXiv:2212.07227
8. M. Hoff, I. Stenger, J. I. Yáñez, Movable cones of complete intersections of multidegree one on products of projective spaces, arXiv:2207.11150
9. 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, arXiv:2202.13814
10. F.-O. Schreyer, I. Stenger, Marked Godeaux surfaces with special bicanonical fibers, arXiv:2201.12065
11. C. Bonnafé, U. Thiel, Computational aspects of Calogero-Moser spaces, Selecta Math. New Ser. 29 (2023), Paper No. 79, arXiv:2112.15495
12. G. Bellamy, J. Schmitt, U. Thiel, On Parabolic Subgroups of Symplectic Reflection Groups, Glasg. Math. J. 65 (2023), no. 2, 401–413, arxiv:2112.01268
13. M. Hoff, I. Stenger, On the numerical dimension of Calabi-Yau 3-folds of Picard number 2, Int. Math. Res. Not. IMRN (2023), no.12, 10736–10758,  arxiv:2111.13521
14. M. Hoff, Giovanni Staglianò, Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors, J. Algebra 611 (2022), 630–650, arXiv:2110.15819
15. M. Hoff, A note on syzygies and normal generation for trigonal curves, arXiv:2108.06106
16. 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, arXiv:2108.00993
17. H. T. A. Nguyen, Michael Hoff, T. L. Hoang, On cylindrical smooth rational Fano fourfolds, J. Korean Math. Soc. 59 (2022), no. 1, 87–103, arXiv:2101.04441
18. G. Bellamy, J. Schmitt, U. Thiel, Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution, Math. Z. 300 (2021), no. 1, 661–681, arXiv:2010.00880
19. F.-O. Schreyer, I. Stenger, An 8-dimensional family of simply connected Godeaux surfaces, Trans. Amer. Math. Soc. 376 (2023), 3419–3443, arXiv:2201.12065
20. 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, arXiv:1911.10954

Since April 2024 Vladimir Lazić is a Principal Investigator (together with Daniele Agostini, Samuel Boissière, Enrica Floris, Andreas Höring, Alex Küronya, Christian Lehn, Gianluca Pacienza and Alessandra Sarti) in the Project POK0: Positivity on K-trivial varieties funded by the Agence nationale de la recherche and the Deutsche Forschungsgemeinschaft.