Elliptic fibrations on a generic Jacobian Kummer surface
By Abhinav Kumar. 2011
72 citations recorded by the source corpus.
We describe all the elliptic fibrations with section on the Kummer surface X of the Jacobian of a very general curve C of genus 2 over an algebraically closed field of characteristic 0, modulo the automorphism group of X and the symmetric group on the Weierstrass points of C. In particular, we compute elliptic parameters and Weierstrass equations for the 25 different fibrations and analyze the reducible fibers and Mordell-Weil lattices. This answers completely a question posed by Kuwata and Shioda in 2008.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/57de97ae4cddae35c6d5c057561f7ee047873685
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Geometry and Topology
- D. Huybrechts
- Noam D. Elkies
- Abhinav Kumar
- E. Markman
- Kieran G. O’Grady
- P. Stellari
- Emanuele Macrì
- Keiji Oguiso
In Mathematical Physics
- D. Huybrechts
- Noam D. Elkies
- Abhinav Kumar
- P. Stellari
- Emanuele Macrì
- E. Markman
- Keiji Oguiso
- Ulrike Riess
Citations in the corpus
- Lectures on K3 Surfaces (2016, methodology): “For Kummer surfaces associated with the Jacobian Jac(C) of a generic genus two curve C this was recently studied in detail by Kumar in [337].”
- K3 surfaces and equations for Hilbert modular surfaces (2012, methodology): “These are the most familiar cases of the 2- and 3-neighbor steps, and the other cases of the 2-neighbor step that are needed are more exhaustively described in [Kumar 2014].”