Publikationen
2024
Begutachteter Zeitschriftenartikel
Proof of a Conjecture of Batyrev and Juny on Gorenstein Polytopes
Nill, Benjamin
In: Discrete & computational geometry - New York, NY : Springer, Bd. 72 (2024), Heft 4, S. 1519-1529
Dissertation
Enumeration and sparsity in algebraic geometry
Kretschmer, Andreas; Nill, Benjamin; Kahle, Thomas
In: Magdeburg: Universitätsbibliothek, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2024, 1 Online-Ressource (VII, 148 Seiten, 1,14 MB) [Literaturverzeichnis: Seite 135-148][Literaturverzeichnis: Seite 135-148]
2023
Begutachteter Zeitschriftenartikel
Thin polytopes - lattice polytopes with vanishing local h*-polynomial
Nill, Benjamin; Borger, Christopher; Kretschmer, Andreas
In: International mathematics research notices - Oxford : Oxford University Press . - 2023
2022
Buchbeitrag
Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces
Hering, Milena; Nill, Benjamin; Süß, Hendrik
In: Facets of algebraic geometry ; 2 - Cambridge: Cambridge University Press; Aluffi, Paolo *1960-* . - 2022, insges. 25 S.
Begutachteter Zeitschriftenartikel
On the maximum dual volume of a canonical Fano polytope
Nill, Benjamin; Baletti, Gabriele; Kasprzyk, Alexander M.
In: Forum of mathematics / Sigma - Cambridge : Cambridge Univ. Press, Bd. 10 (2022), Artikel e109, insges. 19 S.
2020
Begutachteter Zeitschriftenartikel
Gorenstein polytopes with trinomial h -polynomials
Higashitani, Akihiro; Nill, Benjamin; Tsuchiya, Akiyoshi
In: Beiträge zur Algebra und Geometrie - Berlin: Springer . - 2020[Online first]
On defectivity of families of full-dimensional point configurations
Borger, Christopher; Nill, Benjamin
In: Proceedings of the American Mathematical Society / B/ American Mathematical Society - Providence, RI: Soc., Bd. 7 (2020), S. 43-51
The mixed degree of families of lattice polytopes
Nill, Benjamin
In: Annals of combinatorics - [Cham (ZG)]: [Springer International Publishing AG], Bd. 24 (2020), S. 203-216
Dissertation
Mixed lattice polytope theory with a view towards sparse polynomial systems
Borger, Christopher; Nill, Benjamin
In: Magdeburg, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2020, XV, 136 Seiten [Literaturverzeichnis: Seite 109-113][Literaturverzeichnis: Seite 109-113]
2019
Begutachteter Zeitschriftenartikel
A note on discrete mixed volume and Hodge-Deligne numbers
Di Rocco, Sandra; Haase, Christian; Nill, Benjamin
In: Advances in applied mathematics - Amsterdam [u.a.]: Elsevier, 1980, Bd. 104.2019, S. 1-13
Nicht begutachteter Zeitschriftenartikel
Generalized flatness constants, spanning lattice polytopes, and the Gromov width
Averkov, Gennadiy; Hofscheier, Johannes; Nill, Benjamin
In: De.arxiv.org - [S.l.]: Arxiv.org, 1991, 2019, article 1911.03511, 11 Seiten
2018
Begutachteter Zeitschriftenartikel
Lattice simplices with a fixed positive number of interior lattice points - a nearly optimal volume bound
Averkov, Gennadiy; Krümpelmann, Jan; Nill, Benjamin
In: International mathematics research notices: IMRN - Oxford: Oxford University Press, 1991 . - 2018[Online first]
Smooth polytopes with negative Ehrhart coefficients
Castillo, Federico; Liu, Fu; Nill, Benjamin; Paffenholz, Andreas
In: Journal of combinatorial theory / A - Amsterdam [u.a.]: Elsevier, 1971, Bd. 160.2018, S. 316-331
On Ehrhart polynomials of lattice triangles
Hofscheier, Johannes; Nill, Benjamin; Öberg, Dennis
In: The electronic journal of combinatorics - [Madralin]: EMIS ELibEMS, 1994, Vol. 25.2018, 1, Art. P1.3, insgesamt 8 S.
Habilitation
Modern aspects of classical convex geometry
Saorín Gómez, Eugenia; Nill, Benjamin
In: Magdeburg, 2017, xxxii, 153 Seiten, Illustrationen, 30 cm[Literaturverzeichnis: Seite 131-136]
2017
Begutachteter Zeitschriftenartikel
Minimality and mutation-equivalence of polygons
Kasprzyk, Alexander; Nill, Benjamin; Prince, Thomas
In: Forum of mathematics / Sigma - Cambridge: Cambridge Univ. Press, Vol. 5.2017, Art. e18, insgesamt 48 S.
Ehrhart theory of spanning lattice polytopes
Hofscheier, Johannes; Katthän, Lukas; Nill, Benjamin
In: International mathematics research notices : IMRN - Oxford : Oxford University Press, 2017
2015
Begutachteter Zeitschriftenartikel
The degree of point configurations - Ehrhart theory, Tverberg points and almost neighborly polytopes
Nill, Benjamin; Padrol, Arnau
In: European journal of combinatorics - London: Academic Press, Bd. 50.2015, S. 159-179
Finitely many smooth d-polytopes with n lattice points
Bogart, Tristram; Haase, Christian; Hering, Milena; Lorenz, Benjamin; Nill, Benjamin; Paffenholz, Andreas; Rote, Günter; Santos, Francisco; Schenck, Hal
In: Israel journal of mathematics - Berlin: Springer, Bd. 207 (2015), 1, S. 301-329
On smooth {G}orenstein polytopes
Lorenz, Benjamin; Nill, Benjamin
In: Tohoku Math. J. (2), Vol. 67, 2015, Issue 4, S. 513--530, ISSN 0040-8735, 10.2748/tmj/1450798070
Largest integral simplices with one interior integral point - solution of Hensley's conjecture and related results
Averkov, Gennadiy; Krümpelmann, Jan; Nill, Benjamin
In: Advances in mathematics - Amsterdam [u.a.]: Elsevier, 1961, Bd. 274.2015, S. 118-166, 2014
A bound for the splitting of smooth Fano polytopes with many vertices
Assarf, Benjamin; Nill, Benjamin
In: Journal of algebraic combinatorics - Dordrecht [u.a.]: Springer Science + Business Media B.V, 1992 . - 2015, insges. 20 S.
2014
Begutachteter Zeitschriftenartikel
On the equality case in Ehrhart's volume conjecture
Nill, B.; Paffenholz, A.
In: Advances in Geometry, Vol. 14, 2014, Issue 4, S. 579-586, 10.1515/advgeom-2014-0001
Polytopes associated to dihedral groups
Baumeister, B.; Haase, C.; Nill, B.; Paffenholz, A.
In: Ars Mathematica Contemporanea, Vol. 7, 2014, Issue 1, S. 30-38
2013
Buchbeitrag
Fano polytopes
Kasprzyk, Alexander M.; Nill, Benjamin
In: 2013, S. 349--364
Begutachteter Zeitschriftenartikel
Polyhedral adjunction theory
Di Rocco, S.; Haase, C.; Nill, B.; Paffenholz, A.
In: Algebra and Number Theory, Vol. 7, 2013, Issue 10, S. 2417-2446, 10.2140/ant.2013.7.2417
Gorenstein polytopes and their stringy E-functions
Nill, B.; Schepers, J.
In: Mathematische Annalen, Vol. 355, 2013, Issue 2, S. 457-480, 10.1007/s00208-012-0792-2
2012
Buchbeitrag
Permutation polytopes of cyclic groups
Baumeister, B.; Haase, C.; Nill, B.; Paffenholz, A.
In: Discrete Mathematics and Theoretical Computer Science, 2012, S. 421-432
Begutachteter Zeitschriftenartikel
A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes
Dickenstein, A.; Nill, B.; Vergne, M.
In: Comptes Rendus Mathematique, Vol. 350, 2012, Issue 5-6, S. 229-233, 10.1016/j.crma.2012.02.001
Reflexive polytopes of higher index and the number 12
Kasprzyk, A.M.; Nill, B.
In: Electronic Journal of Combinatorics, Vol. 19, 2012, Issue 3, S. 1-18
Lattice-width directions and minkowski's 3 d-theorem
Draisma, J.; McAllister, T.B.; Nill, B.
In: SIAM Journal on Discrete Mathematics, Vol. 26, 2012, Issue 3, S. 1104-1107, 10.1137/120877635
2011
Begutachteter Zeitschriftenartikel
Examples of Kähler-Einstein toric Fano manifolds associated to non-symmetric reflexive polytopes
Nill, B.; Paffenholz, A.
In: Beitrage zur Algebra und Geometrie, Vol. 52, 2011, Issue 2, S. 297-304, 10.1007/s13366-011-0041-y
Projecting lattice polytopes without interior lattice points
Nill, B.; Ziegler, G.M.
In: Mathematics of Operations Research, Vol. 36, 2011, Issue 3, S. 462-467, 10.1287/moor.1110.0503
2010
Begutachteter Zeitschriftenartikel
A simple combinatorial criterion for projective toric manifolds with dual defect
Dickenstein, A.; Nill, B.
In: Mathematical Research Letters, Vol. 17, 2010, Issue 3, S. 435-448
On the combinatorial classification of toric log del {P}ezzo surfaces
Kasprzyk, Alexander M.; Kreuzer, Maximilian; Nill, Benjamin
In: LMS J. Comput. Math., Vol. 13, 2010, S. 33--46, ISSN 1461-1570, 10.1112/S1461157008000387
Q-Factorial gorenstein toric fano varieties with large picard number
Nill, B.; Øbro, M.
In: Tohoku Mathematical Journal, Vol. 62, 2010, Issue 1, S. 1-15
2009
Begutachteter Zeitschriftenartikel
Classification of toric Fano 5-folds
Kreuzer, M.; Nill, B.
In: Advances in Geometry, Vol. 9, 2009, Issue 1, S. 85-97, 10.1515/ADVGEOM.2009.005
On permutation polytopes
Baumeister, B.; Haase, C.; Nill, B.; Paffenholz, A.
In: Advances in Mathematics, Vol. 222, 2009, Issue 2, S. 431-452, 10.1016/j.aim.2009.05.003
Flow polytopes and the graph of reflexive polytopes
Altmann, K.; Nill, B.; Schwentner, S.; Wiercinska, I.
In: Discrete Mathematics, Vol. 309, 2009, Issue 16, S. 4992-4999, 10.1016/j.disc.2009.03.001
Cayley decompositions of lattice polytopes and upper bounds for h-polynomials
Haase, C.; Nill, B.; Payne, S.
In: Journal fur die Reine und Angewandte Mathematik, 2009, Issue 637, S. 207-216, 10.1515/CRELLE.2009.096
2008
Buchbeitrag
Combinatorial aspects of mirror symmetry
Batyrev, Victor; Nill, Benjamin
In: Vol. 452, 2008, S. 35--66, 10.1090/conm/452/08770
Let me tell you my favorite lattice-point problem {$\dots$}
Beck, Matthias; Nill, Benjamin; Reznick, Bruce; Savage, Carla; Soprunov, Ivan; Xu, Zhiqiang
In: Vol. 452, 2008, S. 179--187, 10.1090/conm/452/08782
Begutachteter Zeitschriftenartikel
Stanley's conjecture, cover depth and extremal simplicial complexes
Nill, Benjamin; Vorwerk, Kathrin
In: Matematiche (Catania), Vol. 63, 2008, Issue 2, S. 213--228 (2009), ISSN 0373-3505
Lattice polytopes having h*-polynomials with given degree and linear coefficient
Nill, B.
In: European Journal of Combinatorics, Vol. 29, 2008, Issue 7, S. 1596-1602, 10.1016/j.ejc.2007.11.002
Lattices generated by skeletons of reflexive polytopes
Haase, C.; Nill, B.
In: Journal of Combinatorial Theory. Series A, Vol. 115, 2008, Issue 2, S. 340-344, 10.1016/j.jcta.2007.05.003
Lattice points in Minkowski sums
Haase, C.; Nill, B.; Paffenholz, A.; Santos, F.
In: Electronic Journal of Combinatorics, Vol. 15, 2008, Issue 1 N
A boundedness result for toric log Del Pezzo surfaces
Dais, D.I.; Nill, B.
In: Archiv der Mathematik, Vol. 91, 2008, Issue 6, S. 526-535, 10.1007/s00013-008-2913-4
2007
Begutachteter Zeitschriftenartikel
Multiples of lattice polytopes without interior lattice points
Batyrev, Victor; Nill, Benjamin
In: Mosc. Math. J., Vol. 7, 2007, Issue 2, S. 195--207, 349, ISSN 1609-3321
Volume and lattice points of reflexive simplices
Nill, B.
In: Discrete and Computational Geometry, Vol. 37, 2007, Issue 2, S. 301-320, 10.1007/s00454-006-1299-y
2006
Buchbeitrag
Classification of pseudo-symmetric simplicial reflexive polytopes
Nill, Benjamin
In: Algebraic and geometric combinatorics - Euroconference in Mathematics, Algebraic and Geometric Combinatorics, August 20 - 26, 2005, Anogia, Crete, Greece: Euroconference in Mathematics, Algebraic and Geometric Combinatorics, August 20 - 26, 2005, Anogia, Crete, Greece/ Euroconference Algebraic and Geometric Combinatorics - Providence, RI: American Mathematical Society . - 2006, S. 269-282
Begutachteter Zeitschriftenartikel
Complete toric varieties with reductive automorphism group
Nill, B.
In: Mathematische Zeitschrift, Vol. 252, 2006, Issue 4, S. 767-786, 10.1007/s00209-005-0880-z
2005
Begutachteter Zeitschriftenartikel
Gorenstein toric Fano varieties
Nill, B.
In: Manuscripta Mathematica, Vol. 116, 2005, Issue 2, S. 183-210, 10.1007/s00229-004-0532-3