Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Refined broccoli invariants


Authors: Lothar Göttsche and Franziska Schroeter
Journal: J. Algebraic Geom. 28 (2019), 1-41
DOI: https://doi.org/10.1090/jag/705
Published electronically: July 27, 2018
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Abstract | References | Additional Information

Abstract: We introduce a tropical enumerative invariant depending on a variable $ y$ which generalizes the tropical refined Severi degree. We show that this refined broccoli invariant is indeed independent of the point configuration, and that it specializes to a tropical descendant Gromov-Witten invariant for $ y=1$ and to the corresponding broccoli invariant for $ y=-1$. Furthermore, we define tropical refined descendant Gromov-Witten invariants which equal the corresponding refined broccoli invariants giving a new insight to the nature of broccoli invariants. We discuss various possible generalizations e.g. to refinements of bridge curves and Welschinger curves.


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Additional Information

Lothar Göttsche
Affiliation: International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
Email: gottsche@ictp.it

Franziska Schroeter
Affiliation: Fachbereich Mathematik (AD), Universitát Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
Email: franziska.schroeter@uni-hamburg.de

DOI: https://doi.org/10.1090/jag/705
Received by editor(s): August 4, 2016
Received by editor(s) in revised form: April 14, 2017, and April 27, 2017
Published electronically: July 27, 2018
Additional Notes: The second author was partially supported by GIF grant No. 1174-197.6/2011, the Minkowski-Minerva Center for Geometry at the Tel Aviv University, by grant No. 178/13 from the Israel Science Foundation, and by the RTG 1670 “Mathematics Inspired by String Theory and Quantum Field Theory” funded by the German Research Foundation (DFG)
Article copyright: © Copyright 2018 University Press, Inc.

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