256 citations · 779 across the 26 of their papers we have counts for
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math.AG2014★ 25 cited
Hilbert modular surfaces for square discriminants and elliptic subfields of genus 2 function fields
Abhinav Kumar
We compute explicit rational models for some Hilbert modular surfaces corresponding to square discriminants, by connecting them to moduli spaces of elliptic K3 surfaces. Since they…
math.AG2014★ 6 cited
Elliptic K3 surfaces associated with the product of two elliptic curves: Mordell-Weil lattices and their fields of definition
Abhinav Kumar, Masato Kuwata
To a pair of elliptic curves, one can naturally attach two K3 surfaces: the Kummer surface of their product and a double cover of it, called the Inose surface. They have prominentl…
math.AG2014★ 9 cited
Algebraic models and arithmetic geometry of Teichmüller curves in genus two
Abhinav Kumar, Ronen E. Mukamel
A Teichmüller curve is an algebraic and isometric immersion of an algebraic curve into the moduli space of Riemann surfaces. We give the first explicit algebraic models of Teichmül…