# Maksym Fedorchuk

Associate Professor

Email: fedorchm[at]bc.edu
Tel: 617-552-3757

Department of Mathematics
Boston College
Maloney Hall 570
140 Commonwealth Avenue
Chestnut Hill, MA 02467

### Curriculum Vitae

Announcements:
1. AGNBC Spring 2019 one-day AG-near-Boston conference at MIT, April 27, 2019.
2. Fall 2019 AGNES (AG NorthEast Series) meeting at Boston College, September 20-22, 2019
Recent and future events:
1. COW Workshop in algebraic geometry, Cambridge, UK, February 2019.
2. Workshop in algebraic geometry, Princeton, December 2018.
3. Moduli Spaces: Birational Geometry and Wall Crossings:
Standard models of low degree del Pezzo fibrations and GIT for syzygy points, Banff, October 2018.

### Research

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

#### Publications and preprints

1. Standard models of low degree del Pezzo fibrations, with Hamid Ahmadinezhad and Igor Krylov, coming soon.

2. Associated form morphism (joint with Alexander Isaev), preprint on arXiv:1807.02082 ,
International Mathematics Research Notices, doi.org/10.1093/imrn/rnz060, online publication March 2019, 23pp.

3. VGIT presentation of the second flip of $\overline{M}_{2,1}$ (joint with Matthew Grimes), preprint on arXiv:1805.08581,
to appear in Michigan Math Journal, revision as of November 2018, 26pp.

4. Geometric Invariant Theory of syzygies, with applications to moduli spaces, preprint on arXiv:1712.02776
in Abel Symposia: Geometry of moduli, 14 (2018), 107--134.

5. Direct sum decomposability of polynomials and factorization of associated forms (revision as of November 2018), preprint on arXiv:1705.03452, submitted, 25pp.
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.

6. Stability of associated forms (joint with Alexander Isaev) on arXiv:1703.00438
Journal of Algebraic Geometry, doi.org/10.1090/jag/719, online publication May 2019, 22pp.

7. GIT semistability of Hilbert points of Milnor algebras on arXiv:1508.06991
Math. Ann. 367 (2017), no. 1-2, 441-460 (journal version).

8. 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.

9. 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).

10. 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).

11. 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)

12. 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)

13. Groebner techniques and ribbons (joint with Anand Deopurkar and David Swinarski),
Albanian J. Math. 8 (2014), no. 2, 55-70 (journal version)

14. 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.

15. 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)

16. 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.

17. Moduli spaces of hyperelliptic curves with A and D singularities
Mathematische Zeitschrift 276 (2013) no. 1--2, 299-328 (journal version)

18. 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 www.springerlink.com

19. Stability of 2nd Hilbert points of canonical curves (joint with David Jensen)
Int. Math. Res. Notices, 2013 (2013) no. 22: 5270-5287 (journal version)

20. 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)

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

22. 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

23. 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)

24. Ample divisors on moduli spaces of pointed rational curves (joint with David Smyth)
J. Algebraic Geom., 20 (2011) no. 4, 599-629 (journal version)

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

26. Rigidity and polynomial invariants of convex polytopes (joint with Igor Pak)
Duke Math. J., 129 (2005), no. 2, 371-404 (journal version)