Publications Hannah

From CRCG-Wiki

Contents 1 Publications by Hannah Markwig 1.1 Preprints 1.2 To appear 1.3 Published Articles 1.4 Survey 1.5 Diplom thesis 1.6 PhD thesis 1.7 tropical SINGULAR-libraries

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 M_0,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).