Publikationen

2019

Begutachteter Zeitschriftenartikel

Di Rocco, Sandra;  Haase, Christian;  Nill, Benjamin 

A note on discrete mixed volume and Hodge-Deligne numbers
In: Advances in applied mathematics - Amsterdam [u.a.]: Elsevier, Bd. 104.2019, S. 1-13

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2018

Begutachteter Zeitschriftenartikel

Averkov, Gennadiy;  Krümpelmann, Jan;  Nill, Benjamin 

Lattice simplices with a fixed positive number of interior lattice points - a nearly optimal volume bound
In: International mathematics research notices: IMRN - Oxford: Oxford University Press, 2018

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Hofscheier, Johannes;  Nill, Benjamin;  Öberg, Dennis 

On Ehrhart polynomials of lattice triangles
In: The electronic journal of combinatorics - [Madralin]: EMIS ELibEMS, Vol. 25.2018, 1, Art. P1.3, insgesamt 8 S.

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Castillo, Federico;  Liu, Fu;  Nill, Benjamin;  Paffenholz, Andreas 

Smooth polytopes with negative Ehrhart coefficients
In: Journal of combinatorial theory / A - Amsterdam [u.a.]: Elsevier, Bd. 160.2018, S. 316-331

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Habilitation

Saorín Gómez, Eugenia;  Nill, Benjamin [GutachterIn] 

Modern aspects of classical convex geometry
In: Magdeburg, 2017, xxxii, 153 Seiten, Illustrationen, 30 cm ; [Literaturverzeichnis: Seite 131-136]

2017

Begutachteter Zeitschriftenartikel

Hofscheier, Johannes;  Katthän, Lukas;  Nill, Benjamin 

Ehrhart theory of spanning lattice polytopes
In: International mathematics research notices: IMRN - Oxford: Oxford University Press, 2017

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Kasprzyk, Alexander;  Nill, Benjamin;  Prince, Thomas 

Minimality and mutation-equivalence of polygons
In: Forum of mathematics / Sigma - Cambridge: Cambridge Univ. Press, Vol. 5.2017, Art. e18, insgesamt 48 S.

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2015

Begutachteter Zeitschriftenartikel

Assarf, Benjamin;  Nill, Benjamin 

A bound for the splitting of smooth Fano polytopes with many vertices
In: Journal of algebraic combinatorics: an international journal - Dordrecht [u.a.]: Springer Science + Business Media B.V, insges. 20 S., 2015

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Bogart, Tristram;  Haase, Christian;  Hering, Milena;  Lorenz, Benjamin;  Nill, Benjamin;  Paffenholz, Andreas;  Rote, Günter;  Santos, Francisco;  Schenck, Hal 

Finitely many smooth d-polytopes with n lattice points
In: Israel journal of mathematics - Berlin: Springer, Bd. 207.2015, 1, S. 301-329

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Averkov, Gennadiy;  Krümpelmann, Jan;  Nill, Benjamin 

Largest integral simplices with one interior integral point - solution of Hensley's conjecture and related results
In: Advances in mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 274.2015, S. 118-166, 2014

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Lorenz, Benjamin;  Nill, Benjamin 

On smooth {G}orenstein polytopes
In: Tohoku Math. J. (2), Vol. 67, 2015, Issue 4, S. 513--530, ISSN 0040-8735, 10.2748/tmj/1450798070

Nill, Benjamin;  Padrol, Arnau 

The degree of point configurations - Ehrhart theory, Tverberg points and almost neighborly polytopes
In: European journal of combinatorics - London: Academic Press, Bd. 50.2015, S. 159-179

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2014

Begutachteter Zeitschriftenartikel

Nill, B.;  Paffenholz, A. 

On the equality case in Ehrhart's volume conjecture
In: Advances in Geometry, Vol. 14, 2014, Issue 4, S. 579-586, 10.1515/advgeom-2014-0001

Baumeister, B.;  Haase, C.;  Nill, B.;  Paffenholz, A. 

Polytopes associated to dihedral groups
In: Ars Mathematica Contemporanea, Vol. 7, 2014, Issue 1, S. 30-38

2013

Begutachteter Zeitschriftenartikel

Nill, B.;  Schepers, J. 

Gorenstein polytopes and their stringy E-functions
In: Mathematische Annalen, Vol. 355, 2013, Issue 2, S. 457-480, 10.1007/s00208-012-0792-2

Di Rocco, S.;  Haase, C.;  Nill, B.;  Paffenholz, A. 

Polyhedral adjunction theory
In: Algebra and Number Theory, Vol. 7, 2013, Issue 10, S. 2417-2446, 10.2140/ant.2013.7.2417

Buchbeitrag

Kasprzyk, Alexander M.;  Nill, Benjamin 

Fano polytopes
In: 2013, S. 349--364

2012

Begutachteter Zeitschriftenartikel

Dickenstein, A.;  Nill, B.;  Vergne, M. 

A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes
In: Comptes Rendus Mathematique, Vol. 350, 2012, Issue 5-6, S. 229-233, 10.1016/j.crma.2012.02.001

Draisma, J.;  McAllister, T.B.;  Nill, B. 

Lattice-width directions and minkowski's 3 d-theorem
In: SIAM Journal on Discrete Mathematics, Vol. 26, 2012, Issue 3, S. 1104-1107, 10.1137/120877635

Kasprzyk, A.M.;  Nill, B. 

Reflexive polytopes of higher index and the number 12
In: Electronic Journal of Combinatorics, Vol. 19, 2012, Issue 3, S. 1-18

Buchbeitrag

Baumeister, B.;  Haase, C.;  Nill, B.;  Paffenholz, A. 

Permutation polytopes of cyclic groups
In: Discrete Mathematics and Theoretical Computer Science, 2012, S. 421-432

2011

Begutachteter Zeitschriftenartikel

Nill, B.;  Paffenholz, A. 

Examples of Kähler-Einstein toric Fano manifolds associated to non-symmetric reflexive polytopes
In: Beitrage zur Algebra und Geometrie, Vol. 52, 2011, Issue 2, S. 297-304, 10.1007/s13366-011-0041-y

Nill, B.;  Ziegler, G.M. 

Projecting lattice polytopes without interior lattice points
In: Mathematics of Operations Research, Vol. 36, 2011, Issue 3, S. 462-467, 10.1287/moor.1110.0503

2010

Begutachteter Zeitschriftenartikel

Dickenstein, A.;  Nill, B. 

A simple combinatorial criterion for projective toric manifolds with dual defect
In: Mathematical Research Letters, Vol. 17, 2010, Issue 3, S. 435-448

Kasprzyk, Alexander M.;  Kreuzer, Maximilian;  Nill, Benjamin 

On the combinatorial classification of toric log del {P}ezzo surfaces
In: LMS J. Comput. Math., Vol. 13, 2010, S. 33--46, ISSN 1461-1570, 10.1112/S1461157008000387

Nill, B.;  Øbro, M. 

Q-Factorial gorenstein toric fano varieties with large picard number
In: Tohoku Mathematical Journal, Vol. 62, 2010, Issue 1, S. 1-15

2009

Begutachteter Zeitschriftenartikel

Haase, C.;  Nill, B.;  Payne, S. 

Cayley decompositions of lattice polytopes and upper bounds for h-polynomials
In: Journal fur die Reine und Angewandte Mathematik, 2009, Issue 637, S. 207-216, 10.1515/CRELLE.2009.096

Kreuzer, M.;  Nill, B. 

Classification of toric Fano 5-folds
In: Advances in Geometry, Vol. 9, 2009, Issue 1, S. 85-97, 10.1515/ADVGEOM.2009.005

Altmann, K.;  Nill, B.;  Schwentner, S.;  Wiercinska, I. 

Flow polytopes and the graph of reflexive polytopes
In: Discrete Mathematics, Vol. 309, 2009, Issue 16, S. 4992-4999, 10.1016/j.disc.2009.03.001

Baumeister, B.;  Haase, C.;  Nill, B.;  Paffenholz, A. 

On permutation polytopes
In: Advances in Mathematics, Vol. 222, 2009, Issue 2, S. 431-452, 10.1016/j.aim.2009.05.003

2008

Begutachteter Zeitschriftenartikel

Dais, D.I.;  Nill, B. 

A boundedness result for toric log Del Pezzo surfaces
In: Archiv der Mathematik, Vol. 91, 2008, Issue 6, S. 526-535, 10.1007/s00013-008-2913-4

Haase, C.;  Nill, B.;  Paffenholz, A.;  Santos, F. 

Lattice points in Minkowski sums
In: Electronic Journal of Combinatorics, Vol. 15, 2008, Issue 1 N

Nill, B. 

Lattice polytopes having h*-polynomials with given degree and linear coefficient
In: European Journal of Combinatorics, Vol. 29, 2008, Issue 7, S. 1596-1602, 10.1016/j.ejc.2007.11.002

Haase, C.;  Nill, B. 

Lattices generated by skeletons of reflexive polytopes
In: Journal of Combinatorial Theory. Series A, Vol. 115, 2008, Issue 2, S. 340-344, 10.1016/j.jcta.2007.05.003

Nill, Benjamin;  Vorwerk, Kathrin 

Stanley's conjecture, cover depth and extremal simplicial complexes
In: Matematiche (Catania), Vol. 63, 2008, Issue 2, S. 213--228 (2009), ISSN 0373-3505

Buchbeitrag

Batyrev, Victor;  Nill, Benjamin 

Combinatorial aspects of mirror symmetry
In: Vol. 452, 2008, S. 35--66, 10.1090/conm/452/08770

Beck, Matthias;  Nill, Benjamin;  Reznick, Bruce;  Savage, Carla;  Soprunov, Ivan;  Xu, Zhiqiang 

Let me tell you my favorite lattice-point problem {$\dots$}
In: Vol. 452, 2008, S. 179--187, 10.1090/conm/452/08782

2007

Begutachteter Zeitschriftenartikel

Batyrev, Victor;  Nill, Benjamin 

Multiples of lattice polytopes without interior lattice points
In: Mosc. Math. J., Vol. 7, 2007, Issue 2, S. 195--207, 349, ISSN 1609-3321

Nill, B. 

Volume and lattice points of reflexive simplices
In: Discrete and Computational Geometry, Vol. 37, 2007, Issue 2, S. 301-320, 10.1007/s00454-006-1299-y

2006

Begutachteter Zeitschriftenartikel

Nill, B. 

Complete toric varieties with reductive automorphism group
In: Mathematische Zeitschrift, Vol. 252, 2006, Issue 4, S. 767-786, 10.1007/s00209-005-0880-z

Buchbeitrag

Nill, Benjamin 

Classification of pseudo-symmetric simplicial reflexive polytopes
In: Algebraic and geometric combinatorics : Euroconference in Mathematics, Algebraic and Geometric Combinatorics, August 20 - 26, 2005, Anogia, Crete, Greece. - Providence, RI : American Mathematical Society, S. 269-282, 2006

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2005

Begutachteter Zeitschriftenartikel

Nill, B. 

Gorenstein toric Fano varieties
In: Manuscripta Mathematica, Vol. 116, 2005, Issue 2, S. 183-210, 10.1007/s00229-004-0532-3