Diane Maclagan's publications
Books:
Preprints:
 Toric and tropical Bertini theorems in positive
characteristic. With Francesca Gandini, Milena Hering, Fatemeh
Mohammadi, Jenna Rajchgot, Ashley K. Wheeler, and Josephine Yu. arXiv:2111.13214.

The spine of the Tgraph of the Hilbert scheme of points in the
plane. With Rob Silversmith. arXiv:2111.00819.

Varieties of Tropical Ideals are Balanced. With Felipe
Rincón. arXiv:2009.14557. To appear in Advances in Mathematics

The Cox ring of \overline{M}_{0,6}. With Martha Bernal
Guillén. arXiv:1712.081293.

Computing Tropical Varieties in Macaulay2. With Carlos
Améndola, Kathlén Kohn, Sara Lamboglia, Ben Smith, Jeff
Sommars, Paolo Tripoli, and Magdalena Zajaczkowska. arXiv:1710.10651.
Publications:
 Higher Connectivity of Tropicalizations. With Josephine Yu. arXiv:1908.05988 To appear in Math. Annal.
DOI
 Tropical ideals (with Felipe Rincón). arXiv:1609.03838.
Compositio Mathematica , Volume 154 , Issue 3 , March 2018 , pp. 640  670
 Tropical schemes, tropical cycles, and valuated matroids
(with Felipe Rincón). arXiv:1401.4654.
Journal of the European Mathematical Society, Volume 22, Issue 3, 2020, pp777706
 Gröbner bases over fields with valuations. With Andrew Chan. arxiv.1303.0729. The accompanying Macaulay 2 package is available here.
Math. Comp. 88 (2019), 467483
 Polyhedral structures on tropical
varieties. Mostly survey article for the Bellairs
proceedings.
arxiv.1302.5372. AMS Contemporary Mathematics Volume
Tropical and NonArchimedean Geometry
 Introduction to tropical
algebraic geometry. Survey article. arxiv.1207.1925.
AMS Contemporary Mathematics Volume "Tropical Geometry and
Integrable Systems".
 The Tgraph of
a multigraded Hilbert scheme
arXiv.1110.1861. With Milena Hering. Experimental Mathematics, 21, no 3, 280297, 2012.
The accompanying Macaulay 2 package is available here.
 Lower and upper bounds for nef
cones.
arXiv.1009.0220.
With Angela Gibney. The
accompanying Macaulay 2 package is available here. To appear in IMRN (doi: 10.1093/imrn/rnr121)

Equations for Chow and Hilbert quotients.
arXiv.0707.1801.
With Angela Gibney.
Journal of Algebra and Number Theory, 4 (2010), No 7, 855885.

Smooth and irreducible multigraded Hilbert schemes.
Advances in Mathematics, 223 (2010) 16081631. arXiv.0811.3594.
With Greg
Smith.

Some cases of the
EisenbudGreenHarris conjecture.
Math. Res. Lett. 15 (2008), no 3, 427433.
math.AC/0611488.
With Giulio Caviglia.

Fiber fans and toric quotients
Discrete and Computational Geometry, 37, 251266, 2007. math.AG/0510128.
With Alastair
Craw.

Moduli of McKay quiver representations I: The
coherent component.
Proceedings
of the LMS, 95, 179198, 2007. math.AG/0505115.
With Alastair
Craw and Rekha
R. Thomas.

Moduli of McKay quiver representations II: Grobner
basis techniques.
Journal of Algebra, 316, 2,
515535, 2007 (Computational Algebra section).
math.AG/0611840.
With Alastair
Craw and Rekha
R. Thomas.

The
card game Set.
The Mathematical Intelligencer, 25, No. 3, 2003, 3340.
With Ben Davis.

Multigraded CastelnuovoMumford Regularity..
Journal für die reine und angewandte Mathematik (Crelle's
Journal), 571, (2004), 179212.. math.AC/0305214.
With Greg
Smith.

Uniform Bounds on Multigraded Regularity.
Journal of Algebraic Geometry, 14, no. 1, 2005, 137164.
math.AG/0305215.
With Greg
Smith.

The toric Hilbert scheme of a rank two lattice is smooth and irreducible.
Journal of Combinatorial Theory, Series A, 104, no.1, (2003), 2948.
math.AG/0208031. With Rekha
Thomas .

Supernormal Vector Configurations.
Journal of Algebraic Combinatorics, 19, no. 3, (2004), 297313.
math.CO/0105036.
With Serkan Hosten and Bernd
Sturmfels .

The Vertex Ideal of a Lattice.
Advances in Applied Mathematics, 29, 2002, 521538. math.CO/0012197.
With Serkan Hosten .

Combinatorics of the toric Hilbert scheme
Discrete and Computational Geometry, 27, 2002, no. 2, 249272.
math.AG.9912014.
With Rekha Thomas .
 Antichains of
Monomial Ideals are Finite.
Proceedings of the AMS, 129, 2001, no. 6, 16091615.
math.CO.9909168.
 Boolean Term
Orders and the Root System B_n.
Order 15 (3):279295, 1998. math.CO.9809134.
 Equivalent
methods for global optimization.
In State of the art in global
optimization (Princeton, NJ, 1995), 201211, Nonconvex Optim. Appl.,
7,
Kluwer Acad. Publ., Dordrecht, 1996.
With Timothy Sturge
and
William Baritompa .
Software:
Lecture Notes:
 Notes on Hilbert schemes.
Lecture notes from five lectures on
Hilbert schemes given at the Summer School on
Introduction to explicit methods
in algebraic geometry, run September 37, 2007, at the
University of Warwick.

Lecture notes on tropical geometry
from the AARMS
Summer School at UNB in July/August 2008.
 Lecture notes on tropical geometry
from the ELGA 2011 graduate school in Buenos Aires, August 2011.
Videos of the lectures are available here.
 Lecture notes on Tropical
Geometry from the LMS Undergraduate Summer School at the
University of Manchester, July 2017.
 Multigraded Hilbert schemes. Notes from the school on Hilbert schemes, McKay correspondence, and singularities, Paris, 1618 December, 2019.
Dissertation:
Coming soon:
 The tropical inverse problem and cones of effective
cycles.
Search for Maclagan on the xxx preprint
archive or on
MathSciNet .