Maksym Fedorchuk


Email: fedorchm[at]

Tel: 617-552-3757

Department of Mathematics

Boston College

Maloney Hall 570

140 Commonwealth Avenue

Chestnut Hill, MA 02467


I am an algebraic geometer, interested in moduli problems and attendant GIT constructions.

Publications and preprints

29. CM minimizers are standard models of del Pezzo fibrations, with Hamid Abban and Igor Krylov, in preparation, 2024.

28. K-moduli of Fano threefolds of rank 4 and degree 24, with Ivan Cheltsov, Kento Fujita, and Anne-Sophie Kaloghiros, in preparation, 2024.

27. Symmetric F-conjecture for $g\leq 35$, preprint on arXiv:2007.13457

26. Stability of fibrations over one-dimensional bases (joint with Hamid Ahmadinezhad and Igor Krylov), arXiv:1912.08779.

Duke Math. J. 171(12): 2461-2518 (1 September 2022). DOI: 10.1215/00127094-2022-0025 

25. Associated form morphism (joint with Alexander Isaev), arXiv:1807.02082,

International Mathematics Research Notices, 2021, no. 1 (2021), 695--753 (journal version).

24. VGIT presentation of the second flip of $\overline{M}_{2,1}$ (joint with Matthew Grimes), arXiv:1805.08581,

Michigan Math Journal, 69, no. 3 (2020), 487--514 (journal version).

23. Geometric Invariant Theory of syzygies, with applications to moduli spaces, arXiv:1712.02776

in Abel Symposia: Geometry of moduli, 14 (2018), 107--134.

22. Direct sum decomposability of polynomials and factorization of associated forms, arXiv:1705.03452,

Proceedings of the London Mathematical Society, 120, no. 3, (2020), 305–327.

A short Macaulay2 package co-written by Z.Fang and J.Kim (supported by Summer 2017 BC URF) determines if a homogeneous polynomial with a nonzero discriminant over the rationals is a direct sum and computes a direct sum decomposition when it exists.

21. Stability of associated forms (joint with Alexander Isaev) on arXiv:1703.00438

Journal of Algebraic Geometry, 28. no. 4, (2019), 699–720.

20. GIT semistability of Hilbert points of Milnor algebras on arXiv:1508.06991

Math. Ann. 367 (2017), no. 1-2, 441-460.

19. Semiampleness criteria for divisors on $\overline{M}_{0,n}$, submitted, 36pp. An accompanying SAGE worksheet

A major revision (June 2015) of an earlier arXiv:1407.7839 now incorporates new results and Item (13) below.

18. Second flip in the Hassett-Keel program: A local description (joint with Jarod Alper, David Smyth, and Fred van der Wyck)

Compositio Mathematica, 153 (2017), no. 8, 1547-1583 (journal version).

17. Second flip in the Hassett-Keel program: Existence of good moduli spaces (joint with Jarod Alper and David Smyth)

Compositio Mathematica, 153 (2017), no. 8, 1584-1609 (journal version).

16. Second flip in the Hassett-Keel program: Projectivity (joint with Jarod Alper and David Smyth),

International Mathematics Research Notices 2017 (2017), no. 24, 7375-7419 (journal version)

15. Toward GIT stability of syzygies of canonical curves (joint with Anand Deopurkar and David Swinarski) on arXiv:1401.6101

Algebraic Geometry 3 (2016), no. 1, 1-22 (journal version)

14. Groebner techniques and ribbons (joint with Anand Deopurkar and David Swinarski),

Albanian J. Math. 8 (2014), no. 2, 55-70 (journal version)

13. New nef divisors on $\overline{M}_{0,n}$ on arXiv:1308.5993.

Not for publication, subsumed by Item (19) above; contains a precursor of a combinatorial criterion for semiampleness that is used in Item (19) and proves Conjecture 1.7 from the earlier: Type A level one conformal blocks divisors revisited, 2011.

12. Singularities with G_m-action and the log minimal model program for $\overline{M}_g$ (joint with Jarod Alper and David Smyth),

Journal fur die reine und angewandte Mathematik, 2016 (2016), no. 721, 1-41 (journal version)

11. GIT of genus five canonical curves (joint with David Smyth) on arXiv:1302.4804

A Celebration of Algebraic Geometry, 281-310, Clay Mathematics Proceedings, vol. 18, CMI/AMS, 2013.

10. Moduli spaces of hyperelliptic curves with A and D singularities

Mathematische Zeitschrift 276 (2013) no. 1--2, 299-328 (journal version)

9. Finite Hilbert stability of (bi)canonical curves (joint with Jarod Alper and David Smyth)

Inventiones mathematicae 191 (2013) no. 3, 671-718 (journal version)

*The final publication is available at

8. Stability of 2nd Hilbert points of canonical curves (joint with David Jensen)

Int. Math. Res. Notices, 2013 (2013) no. 22: 5270-5287 (journal version)

7. The final log canonical model of the moduli space of stable curves of genus four

Int. Math. Res. Notices, 2012 (2012) no. 24: 5650-5672 (journal version)

6. Cyclic covering morphisms on $\overline{M}_{0,n}$ (with an appendix by Anand Deopurkar, 2013); an older version on arXiv:1105.0655

5. Alternate compactifications of moduli spaces of curves (joint with David Smyth) on arXiv:1012.0329

in Handbook of Moduli: Volume I, 331-414, editors Gavril Farkas and Ian Morrison, Adv. Lect. Math. (ALM), 24, Int. Press, Somerville, MA, 2013

4. Moduli spaces of weighted stable curves and log canonical models of M_{g,n}

Math. Res. Lett., 18 (2011) no. 4, 663-675 (journal version)

3. Ample divisors on moduli spaces of pointed rational curves (joint with David Smyth)

J. Algebraic Geom., 20 (2011) no. 4, 599-629 (journal version)

2. Severi varieties and the moduli space of curves (Harvard dissertation) on arXiv:0710.1623

1. Rigidity and polynomial invariants of convex polytopes (joint with Igor Pak)

Duke Math. J., 129 (2005), no. 2, 371-404 (journal version)