Algebra und Geometrie

Publications

R E S E A R C H   P A P E R S
01. Bounded volume denominators and bounded negativity (with Thomas Bauer, Brian Harbourne, Matthias Nickel), International Mathematics Research Notices, doi:10.1093/imrn/rnz335 . 
02. A Reider-type theorem for higher syzygies on abelian surfaces (with Victor Lozovanu), AlgebraicGeometry 6 (2019), no. 5., 548–570, doi:10.14231/AG-2019-025, (arXiv:1509.08621).
03. Higher syzygies on surfaces with numerically trivial canonical bundle (with Daniele Agostini, Victor Lozovanu), Math. Zeitschrift doi:10.1007/s00209-018-2220-0 (arXiv:1703.10203).
04. Geometric aspects of Newton–Okounkov bodies (with Victor Lozovanu), Phenomenological approach to algebraic geometry (Eds. J. Buczynski, S. Cynk, T. Szemberg) Banach Center Publications 116, Polish Academy of Sciences, Warsaw 2018, 137–212.
05. Continuous CM-regularity of semihomogeneous vector bundles (with Yusuf Mustopa), Advances in Geometry, doi:10.1515/advgeom-2019-0011 (arXiv:1703.07237).
06. Local positivity of linear series on surfaces (with Victor Lozovanu), Algebra & Number Theory Journal 12 (2018), no. 1, 1–34.
07. Infinitesimal Newton–Okounkov bodies and jet separation (with Victor Lozovanu), Duke Mathematical Journal 166 (2017), no. 7, 1349–1376.
08. Positivity of line bundles and Newton–Okounkov bodies (with Victor Lozovanu), Documenta Mathematica 22 (2017), 1285–1302.
09. Rationality of Seshadri constants and the Segre–Harbourne–Gimigliano–Hirschowitz conjecture (with Marcin Dumnicki, Catriona Maclean, Tomasz Szemberg), Advances in Mathematics 303 (2016), 1162–1170.
10. Newton–Okounkov bodies sprouting on the valuative tree (with C. Ciliberto, M. Farnik, V. Lozovanu, J. Roé, C. Shramov), Rendiconti del Circolo Matematico di Palermo II. Ser. 66 (2017), no. 2, 161–194.
11. Seshadri constants via functions on Newton–Okounkov bodies (with Marcin Dumnicki, Catriona Maclean, and Tomasz Szemberg),
to appear in the Mathematische Nachrichten 289 (2016), No. 17–18, 2173–2177.
12. An elementary approach to containment relations between symbolic and ordinary powers of certain monomial ideals (with Ryan W. Keane, Elise MacMahon), Communications in Algebra 45 (2017), no. 11, 4583–4587.
13. On positivity and base loci of vector bundles (with Thomas Bauer, Sándor J. Kovács, Ernesto Carlo Mistretta, Tomasz Szemberg, Stefano Urbinati), European Journal of Math. 1 (2015), no. 2, 229–249.

14.

 Vanishing sequences and Okounkov bodies (with Sébastien Boucksom, Catriona Maclean, and Tomasz Szemberg),
Mathematische Annalen 361, No. 3. (2015), 811–834, doi:10.1007/s00208-014-1081-z.
15. Partial positivity: geometry and cohomology of q-ample line bundles (with Daniel Greb), Recent advances in algebraic geometry, 207–239, London Math. Soc. Lecture Note Ser., 417, Cambridge Univ. Press, Cambridge, 2015. 
16. Very general monomial valuations on P 2 and a Nagata-type conjecture (with Marcin Dumnicki, Brian Harbourne, Joaquim Roé, Tomasz Szemberg), Communications in Analysis and Geometry 25 (2017), no. 1, 125–161.
17. Okounkov bodies of finitely generated divisors (with Dave Anderson and Victor Lozovanu), International Mathematics Research Notices 2014, no. 9, 2343–2355.;DOI: 10.1093/imrn/rns286. 
18. Volume functions of linear series (with Victor Lozovanu and Catriona Maclean), Mathematische Annalen, 356 No. 2. (2013), 635–652, doi: 10.1007/s00208-012-0859-0.
19. Finite generation and geography of models (with Anne-Sophie Kaloghiros and Vladimir Lazić), Minimal models and extremal rays (Kyoto, 2011), 215–245, Adv. Stud. Pure Math., 70, Math. Soc. Japan, Tokyo, 2016.
20. Positivity of restrictions on subvarieties and vanishing of higher cohomology, Annales de l'Institut Fourier 63 (2013), No. 5., 1717–1737.
21. Negative curves on algebraic surfaces (with Th. Bauer, B. Harbourne, A. L. Knutsen, S. Müller-Stach, T. Szemberg), Duke Mathematical Journal, 162 No. 10. (2013), 1877–1894, doi: 10.1215/00127094-2335368.
22. Zariski decompositions of b-divisors (with Catriona Maclean), Mathematische Zeitschrift, 273 (2013), 427–436, doi: 10.1007/s00209-012-1012-1, 2013.
23. Recent developments and open problems in the theory of linear series (with Thomas Bauer, Christiano Bocci, Susan Cooper, Sandra Di Rocco, Marcin Dumnicki, Brian Harbourne, Kelly Jabbusch, Andreas Leopold Knutsen, Rick Miranda, Joaqim Roé, Hal Schenck, Tomasz Szemberg, Zach Teitler), In ''Contributions to Algebraic Geometry'', 93--140, IMPANGA Lecture Notes (Piotr Pragacz , ed.), EMS Series of Congress Reports, edited by the European Mathematical Society Publishing House 2012.
24. Convex bodies appearing as Okounkov bodies of divisors (with Victor Lozovanu and Catriona Maclean), arXiv:1008.4431, Advances in Mathematics 229 (2012), 2622-2639.
25. Higher cohomology of divisors on a projective variety (with Tommaso de Fernex and Robert Lazarsfeld), Mathematische Annalen 337 No. 2. (2007), 443-455.
26. A Briancon--Skoda type theorem for graded systems of ideals (with Alexandre Wolfe), Journal of Algebra 307 No. 2. (2007), 795-803.
27. Asymptotic cohomological functions on projective varieties, American Journal of Mathematics 128 No. 6. (2006) 1475-1519.
28. Asymptotic cohomological functions of toric divisors (with Milena Hering and Sam Payne), Advances in Mathematics 207 No. 2. (2006) 634-645.
29. Zariski decompositions, volumes, and stable base loci (with Thomas Bauer and Tomasz Szemberg), Journal für die reine und angewandte Mathematik 576 (2004), 209-233.
30. A divisorial valuation with irrational volume, Journal of Algebra 262 (2003), 413-423.
31. Computing Levi decompositions in Lie algebras (with Willem de Graaf, Gábor Ivanyos, and Lajos Rónyai), Applicable Algebra in Engineering, Communication and Computing 8 (1997), 291-304.

R E S E A R C H   P A P E R S   S U B M I T T E D   F O R   P U B L I C A T I O N
32. Geometry of multigraded rings and embeddings into toric varieties (with Stefano Urbinati), preprint, arXiv:1912.04374.
33. Concave transforms of filtrations and rationality of Seshadri constants (with Catriona Maclean, Joaquim Roé), preprint, arXiv:1901.00384 (positive referee report from the Transactions of the AMS).
33. Effective global generation on varieties with numerically trivial canonical class (with Yusuf Mustopa), preprint, arXiv:1810.07079.
35. Newton–Okounkov bodies in an abstract setting (with Catriona Maclen, Joaquim Roé).
36. Toric Newton–Okounkov functions with an application tothe rationality of certain Seshadri constants on surfaces (with Christian Haase, Lena Walter), preprint, arXiv:2008.04018.