K3 Surfaces Associated with Curves of Genus Two
By Abhinav Kumar. 2007
59 citations recorded by the source corpus.
It is known ([10, 27]) that there is a unique K3 surface X which corresponds to a genus 2 curve C such that X has a Shioda-Inose structure with quotient birational to the Kummer surface of the Jacobian of C. In this paper we give an explicit realization of X as an elliptic surface over ℙ 1 with specified singular fibers of type II* and III*. We describe how the Weierstrass coefficients are related to the Igusa-Clebsch invariants of C.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6a94f4ac4f47ca1b5d468961572ae017b3fd59f1
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In Applied Mathematics
In Geometry and Topology
- Abhinav Kumar
- Noam D. Elkies
- Charles F. Doran
- Adrian Clingher
- M. Schuett
- T. Shioda
- D. Huybrechts
- Alexander V. Kitaev
Citations in the corpus
- K3 surfaces and equations for Hilbert modular surfaces (2012, methodology): “The main result of [Kumar 2008] is the following.”
- Lattice polarized K3 surfaces and Siegel modular forms (2010, methodology): “Various parts of the construction have also been discussed by Dolgachev (the Appendix Section of [9]) and Kumar [29].”
- Elliptic Surfaces (2009, methodology): “Then we can apply Kumar’s construction [41] to find the Igusa-Klebsch invariants of a family of genus 2-curves.”