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. AGNES 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. Associated form morphism (joint with Alexander Isaev), preprint on arXiv:1807.02082 ,
    to appear in IMRN, revision as of November 2018, 18pp.

  2. 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.

  3. 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.

  4. 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.

  5. Stability of associated forms (joint with Alexander Isaev) on arXiv:1703.00438 (revision as of January 2018)
    to appear in Journal of Algebraic Geometry, 20pp.

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

  7. 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.

  8. 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).

  9. 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).

  10. 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)

  11. 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)

  12. 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.

  14. 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)

  15. 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.

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

  17. 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

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

  19. 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)

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

  21. 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

  22. 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)

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

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

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

Last modified: Sun Mar 10 10:39:04 EDT 2019