Publications
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A. Gathmann, H. Markwig, D. Ochse, Tropical moduli spaces of stable maps
to a curve, Algorithmic and Experimental Methods in Algebra, Geometry,
and Number Theory (editors: Böckle, Decker, Malle), Springer (2018),
287-309, E-print arXiv:1705.08308
pdf
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A. Gathmann, D. Ochse, Moduli spaces of curves in tropical
varieties, Algorithmic and Experimental Methods in Algebra, Geometry,
and Number Theory (editors: Böckle, Decker, Malle), Springer (2018),
253-286, E-print arXiv:1705.07626
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A. L. Birkmeyer, A. Gathmann, Relative realizability of tropical curves
in a plane in the non-constant coefficient case, E-print
arXiv:1412.3035
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A. Gathmann, K. Schmitz, A. L. Winstel, The realizability of curves in a
tropical plane, Discrete and Computational Geometry 57 (2017)
no. 1, 12-55, E-print arXiv:1307.5686
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A. Gathmann, F. Schroeter, Irreducible cycles and points in special
position in moduli spaces for tropical curves, Electronic Journal of
Combinatorics 19 (2012) no. 4, P26, E-print arXiv:1104.3307
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A. Gathmann, H. Markwig, F. Schroeter, Broccoli curves and the tropical
invariance of Welschinger numbers, Advances in Mathematics 240
(2013), 520-574, E-print arXiv:1104.3118
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F. Block, A. Gathmann, H. Markwig, Psi-floor diagrams and a
Caporaso-Harris type recursion, Israel Journal of Mathematics
191 (2012) no. 1, 405-449, E-print arXiv:1003.2067
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A. Gathmann, M. Kerber, H. Markwig, Tropical fans and the moduli spaces
of tropical curves, Compositio Mathematica 145 (2009) no. 1,
173-195, E-print arXiv:0708.2268
pdf
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A. Gathmann, M. Kerber, A Riemann-Roch theorem in tropical geometry,
Mathematische Zeitschrift 259 (2008), 217-230, E-print
math.CO/0612129
pdf
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A. Gathmann, Tropical algebraic geometry, Jahresbericht der DMV
108 (2006) no. 1, 3-32, E-print math.AG/0601322
pdf
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A. Gathmann, H. Markwig, Kontsevich's formula and the WDVV equations in
tropical geometry, Advances in Mathematics 217 (2008), 537-560,
E-print math.AG/0509628
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A. Gathmann, H. Markwig, The Caporaso-Harris formula and plane relative
Gromov-Witten invariants in tropical geometry, Mathematische Annalen
338 (2007), 845-868, E-print math.AG/0504392
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A. Gathmann, H. Markwig, The numbers of tropical plane curves through
points in general position, Journal für die reine und angewandte
Mathematik 602 (2007), 155-177, E-print math.AG/0504390
pdf
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A. Gathmann, Gromov-Witten invariants of hypersurfaces,
Habilitation Thesis, TU Kaiserslautern (2003)
pdf
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A. Gathmann, Topological recursion relations and Gromov-Witten
invariants in higher genus, E-print math.AG/0305361
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A. Gathmann, The number of plane conics 5-fold tangent to a
given curve, Compositio Mathematica 141 (2005), 487-501,
E-print math.AG/0202002
pdf
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A. Gathmann, Relative Gromov-Witten invariants and the mirror
formula, Mathematische Annalen 325 (2003), 393-412,
E-print math.AG/0009190
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A. Gathmann, Absolute and relative Gromov-Witten invariants of
very ample hypersurfaces, Duke Mathematical Journal 115
(2002) no. 2, 171-203, E-print math.AG/9908054
pdf
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A. Gathmann, Gromov-Witten invariants of blow-ups, Journal
of Algebraic Geometry 10 (2001) no. 3, 399-432, E-print
math.AG/9804043
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A. Gathmann, Gromov-Witten and degeneration invariants:
computation and enumerative significance, PhD Thesis, Universität
Hannover (1998)
pdf
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A. Gathmann, Counting rational curves with multiple points
and Gromov-Witten invariants of blow-ups, E-print alg-geom/9609010
pdf
Software
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GROWI: a C++ program for the
computation of Gromov-Witten invariants
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a-tint: a
Polymake library by Simon Hampe for
tropical intersection theory (link to github.com)
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realizationMatroids.lib: a
Singular library by Anna
Lena Winstel for relative realizability questions on tropical fan curves
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realizationMatroidsNC.lib: a
Singular library by Anna
Lena Birkmeyer for relative realizability questions on tropical curves in
the non-constant coefficient case
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broccoli: a
GAP program to compute
(Welschinger and) broccoli invariants as in the paper by A. Gathmann, H.
Markwig, and F. Schroeter: Broccoli curves and the tropical invariance
of Welschinger numbers
pdf
Further Publications of my Research Group
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A. Gross, Intersection theory on tropicalizations of toroidal
embeddings, E-print arXiv:1510.04604
pdf
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F. Gauß, Planar tropical gravitational descendants with one tangency
condition, E-print arXiv:1509.07309
pdf
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L. Allermann, S. Hampe, J. Rau, On rational equivalence in tropical
geometry, E-print arXiv:1408.1537
pdf
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S. Hampe, Combinatorics of tropical Hurwitz cycles, E-print
arXiv:1407.3933
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S. Hampe, Algorithmic aspects of tropical intersection theory,
PhD Thesis, TU Kaiserslautern (2014)
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C. Torchiani, Enumerative geometry of rational and elliptic tropical
curves in $ {\mathbb R}^m $,
PhD Thesis, TU Kaiserslautern (2014)
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A. Gross, Correspondence theorems via tropicalizations of moduli
spaces, E-print arXiv:1406.1999
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A. Gross, Intersection theory on linear subvarieties of toric
varieties, Collectanea Mathematica 66 no. 2 (2015), 175-190,
E-print arXiv:1312.0480
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J. Frels, K. Schmitz, Lower bounds for the number of generic initial
ideals, E-print arXiv:1303.3461
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D. Ochse, Moduli spaces of rational tropical stable maps into smooth
tropical varieties, PhD Thesis, TU Kaiserslautern (2013)
pdf
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G. François, Tropical intersection products and families of tropical
curves, PhD Thesis, TU Kaiserslautern (2012)
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S. Hampe, a-tint: A polymake extension for algorithmic tropical
intersection theory, European Journal of Combinatorics 36C
(2014), 579-607, E-print arXiv:1208.4248
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K. Schmitz, Generic tropical varieties on subvarieties and in the
non-constant coefficient case, E-print arXiv:1108.4268
pdf
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G. François, S. Hampe, Universal families of rational tropical
curves, Canadian Journal of Mathematics 65 (2013), 120-148,
E-print arXiv:1105.1674
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H. Meyer, Intersection theory on tropical toric varieties and
compactifications of tropical parameter spaces, PhD Thesis, TU
Kaiserslautern (2011)
pdf
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G. François, Cocycles on tropical varieties via piecewise
polynomials, Proceedings of the AMS 141 (2013), 481-497,
E-print arXiv:1102.4783
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M. Herold, Tropical orbit spaces and moduli spaces of tropical
curves, PhD Thesis, TU Kaiserslautern (2011)
pdf
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G. François, J. Rau, The diagonal of tropical matroid varieties and
cycle intersections, Collectanea Mathematica 64 no. 2 (2013),
185-210, E-print arXiv:1012.3260
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L. Allermann, Tropical intersection theory, PhD Thesis, TU
Kaiserslautern (2009)
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L. Allermann, Chern classes of tropical vector bundles,
Arkiv för matematik 50 no. 2 (2012), 237-258, E-print
arXiv:0911.2909
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M. Herold, Tropical orbit spaces and the moduli spaces of
elliptic tropical curves, E-print arXiv:0911.1491
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J. Rau, Tropical intersection theory and gravitational descendants,
PhD Thesis, TU Kaiserslautern (2009)
pdf
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L. Allermann, Tropical intersection products on smooth varieties,
Journal of the EMS 14 no. 1 (2012), 107-126,
E-print arXiv:0904.2693
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J. Rau, Intersections on tropical moduli spaces, E-print
arXiv:0812.3678
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M. Kerber, The enumerative geometry of rational and elliptic tropical
curves and a Riemann-Roch theorem in tropical geometry, PhD Thesis, TU
Kaiserslautern (2008)
pdf
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H. Markwig, J. Rau, Tropical descendant Gromov-Witten invariants,
Manuscripta Mathematica 129 (2009) no. 3, 293-335,
E-print arXiv:0809.1102
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M. Franz, H. Markwig, Tropical enumerative invariants of $ {\mathbb F}_0
$ and $ {\mathbb F}_2 $, Advances in Geometry 11 (2011) no. 1,
49-72, E-print arXiv:0808.3452
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M. Kerber, H. Markwig, Intersecting Psi-classes on tropical
$ {\mathcal M}_{0,n} $, International Mathematics Research Notices
2009 (2009) no. 2, 221-240, E-print arXiv:0709.3953
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L. Allermann, J. Rau, First steps in tropical intersection theory,
Mathematische Zeitschrift 264 (2010) no. 3, 633-670, E-print
arXiv:0709.3705
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M. Kerber, H. Markwig, Counting tropical elliptic plane curves with
fixed $j$-invariant, Commentarii Mathematici Helvetici 84 (2009)
no. 2, 387-427, E-print math.AG/0608472
pdf
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H. Markwig, The enumeration of plane tropical curves, PhD Thesis, TU
Kaiserslautern (2006)
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