Publications Hannah
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Publications by Hannah Markwig
Preprints
- Psi-floor diagrams and a Caporaso-Harris type recursion (with Florian Block and Andreas Gathmann).
- Chamber Structure of Double Hurwitz numbers (with Renzo Cavalieri and Paul Johnson).
- Tropical curves with a singularity in a fixed point (with Thomas Markwig and Eugenii Shustin).
To appear
- Tropical Hurwitz numbers (with Renzo Cavalieri and Paul Johnson), to appear in JACO.
- Tropical enumerative invariants of F0 and F2 (with Marina Franz), to appear in Adv. Geom.
Published Articles
- The tropical j-invariant (with Eric Katz and Thomas Markwig), LMS J. Comput. Math. 12, 2009, 275-294.
- Counting tropical elliptic plane curves with fixed j-invariant (with Michael Kerber), Comment. Math. Helv., 84 (2), 2009, 387–427.
- Tropical fans and the moduli space of tropical curves (with Andreas Gathmann and Michael Kerber), Compos. Math. 145 (2009), no. 1, 173-195.
- Tropical descendant Gromov-Witten invariants (with Johannes Rau), Manuscripta Mathematica, volume 129, issue 3 (2009), 293-335, doi: 10.1007/s00229-009-0256-5.
- Intersecting Psi-classes on tropical M0,n (with Michael Kerber), International Mathematics Research Notices 2008; doi: 10.1093/imrn/rnn130.
- The space of tropically collinear points is shellable (with Josephine Yu), Collect. Math. 60,1 (2009), 63-77.
- The j-invariant of a plane tropical cubic (with Eric Katz and Thomas Markwig), Journal of Algebra 320 (2008), 3832-3848.
- Kontsevich's formula and the WDVV equations in tropical geometry (with Andreas Gathmann), Advances in Mathematics 217 (2008), 537-560.
- An algorithm for lifting points in a tropical variety (with Anders Jensen and Thomas Markwig), Collect. Math. 59 (2008), 129-165.
- The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry (with Andreas Gathmann), Mathematische Annalen 338 (2007), 845-868.
- The numbers of tropical plane curves through points in general position (with Andreas Gathmann), J. Reine Angew. Math. 602 (2007), 155-177.
- Free resolutions of fat points on a conic in the projective plane. Rend. Semin. Mat. Torino 63,1 (2005), 63-80. [pdf]
Survey
- Three tropical enumerative problems. Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2007/2008. Lecture notes from the "Courant Colloquia" held at the University of Göttingen, Göttingen, 2004--2005. Edited by Yuri Tschinkel. Universitätsdrucke Göttingen, Göttingen. [pdf]
Diplom thesis
- Free resolutions of fat points on a conic in the projective plane. Diplomarbeit an der Universität Kaiserslautern (2003). [ps.gz]
PhD thesis
- The enumeration of plane tropical curves. PhD thesis. Technische Universität Kaiserslautern (2006). [ps.gz]
tropical SINGULAR-libraries
- tropical.lib (with Anders Jensen and Thomas Markwig), A SINGULAR 3.0 library for computations in tropical geometry (2007).
- jinvariant.lib (with Eric Katz and Thomas Markwig), A SINGULAR 3.0 library for proving statements about the tropical j-invariant (2007).
