Andreas Gathmann

Publications

  1. 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
  2. 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 pdf
  3. A. L. Birkmeyer, A. Gathmann, Relative realizability of tropical curves in a plane in the non-constant coefficient case, E-print arXiv:1412.3035 pdf
  4. 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 pdf
  5. 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 pdf
  6. 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 pdf
  7. 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 pdf
  8. 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
  9. A. Gathmann, M. Kerber, A Riemann-Roch theorem in tropical geometry, Mathematische Zeitschrift 259 (2008), 217-230, E-print math.CO/0612129 pdf
  10. A. Gathmann, Tropical algebraic geometry, Jahresbericht der DMV 108 (2006) no. 1, 3-32, E-print math.AG/0601322 pdf
  11. 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 pdf
  12. 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 pdf
  13. 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
  14. A. Gathmann, Gromov-Witten invariants of hypersurfaces, Habilitation Thesis, TU Kaiserslautern (2003) pdf
  15. A. Gathmann, Topological recursion relations and Gromov-Witten invariants in higher genus, E-print math.AG/0305361 pdf
  16. 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
  17. A. Gathmann, Relative Gromov-Witten invariants and the mirror formula, Mathematische Annalen 325 (2003), 393-412, E-print math.AG/0009190 pdf
  18. 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
  19. A. Gathmann, Gromov-Witten invariants of blow-ups, Journal of Algebraic Geometry 10 (2001) no. 3, 399-432, E-print math.AG/9804043 pdf
  20. A. Gathmann, Gromov-Witten and degeneration invariants: computation and enumerative significance, PhD Thesis, Universität Hannover (1998) pdf
  21. A. Gathmann, Counting rational curves with multiple points and Gromov-Witten invariants of blow-ups, E-print alg-geom/9609010 pdf

Software

  1. GROWI: a C++ program for the computation of Gromov-Witten invariants
  2. a-tint: a Polymake library by Simon Hampe for tropical intersection theory (link to github.com)
  3. realizationMatroids.lib: a Singular library by Anna Lena Winstel for relative realizability questions on tropical fan curves
  4. realizationMatroidsNC.lib: a Singular library by Anna Lena Birkmeyer for relative realizability questions on tropical curves in the non-constant coefficient case
  5. 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

  1. A. Gross, Intersection theory on tropicalizations of toroidal embeddings, E-print arXiv:1510.04604 pdf
  2. F. Gauß, Planar tropical gravitational descendants with one tangency condition, E-print arXiv:1509.07309 pdf
  3. L. Allermann, S. Hampe, J. Rau, On rational equivalence in tropical geometry, E-print arXiv:1408.1537 pdf
  4. S. Hampe, Combinatorics of tropical Hurwitz cycles, E-print arXiv:1407.3933 pdf
  5. S. Hampe, Algorithmic aspects of tropical intersection theory, PhD Thesis, TU Kaiserslautern (2014) pdf
  6. C. Torchiani, Enumerative geometry of rational and elliptic tropical curves in $ {\mathbb R}^m $, PhD Thesis, TU Kaiserslautern (2014) pdf
  7. A. Gross, Correspondence theorems via tropicalizations of moduli spaces, E-print arXiv:1406.1999 pdf
  8. A. Gross, Intersection theory on linear subvarieties of toric varieties, Collectanea Mathematica 66 no. 2 (2015), 175-190, E-print arXiv:1312.0480 pdf
  9. J. Frels, K. Schmitz, Lower bounds for the number of generic initial ideals, E-print arXiv:1303.3461 pdf
  10. D. Ochse, Moduli spaces of rational tropical stable maps into smooth tropical varieties, PhD Thesis, TU Kaiserslautern (2013) pdf
  11. G. François, Tropical intersection products and families of tropical curves, PhD Thesis, TU Kaiserslautern (2012) pdf
  12. 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 pdf
  13. K. Schmitz, Generic tropical varieties on subvarieties and in the non-constant coefficient case, E-print arXiv:1108.4268 pdf
  14. G. François, S. Hampe, Universal families of rational tropical curves, Canadian Journal of Mathematics 65 (2013), 120-148, E-print arXiv:1105.1674 pdf
  15. H. Meyer, Intersection theory on tropical toric varieties and compactifications of tropical parameter spaces, PhD Thesis, TU Kaiserslautern (2011) pdf
  16. G. François, Cocycles on tropical varieties via piecewise polynomials, Proceedings of the AMS 141 (2013), 481-497, E-print arXiv:1102.4783 pdf
  17. M. Herold, Tropical orbit spaces and moduli spaces of tropical curves, PhD Thesis, TU Kaiserslautern (2011) pdf
  18. 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 pdf
  19. L. Allermann, Tropical intersection theory, PhD Thesis, TU Kaiserslautern (2009) pdf
  20. L. Allermann, Chern classes of tropical vector bundles, Arkiv för matematik 50 no. 2 (2012), 237-258, E-print arXiv:0911.2909 pdf
  21. M. Herold, Tropical orbit spaces and the moduli spaces of elliptic tropical curves, E-print arXiv:0911.1491 pdf
  22. J. Rau, Tropical intersection theory and gravitational descendants, PhD Thesis, TU Kaiserslautern (2009) pdf
  23. L. Allermann, Tropical intersection products on smooth varieties, Journal of the EMS 14 no. 1 (2012), 107-126, E-print arXiv:0904.2693 pdf
  24. J. Rau, Intersections on tropical moduli spaces, E-print arXiv:0812.3678 pdf
  25. 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
  26. H. Markwig, J. Rau, Tropical descendant Gromov-Witten invariants, Manuscripta Mathematica 129 (2009) no. 3, 293-335, E-print arXiv:0809.1102 pdf
  27. 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 pdf
  28. 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 pdf
  29. L. Allermann, J. Rau, First steps in tropical intersection theory, Mathematische Zeitschrift 264 (2010) no. 3, 633-670, E-print arXiv:0709.3705 pdf
  30. 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
  31. H. Markwig, The enumeration of plane tropical curves, PhD Thesis, TU Kaiserslautern (2006) pdf

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