256 citations · 779 across the 26 of their papers we have counts for
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Correspondences for hyperkähler varieties with large Picard numbers
Ljudmila Kamenova, Abhinav Kumar
In this note, we explore the connection between hyperkähler manifolds with large Picard numbers and abelian varieties. In particular, we are interested in Morrison's solution to th…
Inose's construction and elliptic K3 surfaces with Mordell-Weil rank 15 revisited
Abhinav Kumar, Masato Kuwata
We describe two constructions of elliptic K3 surfaces starting from the Kummer surface of the Jacobian of a genus 2 curve. These parallel the base-change constructions of Kuwata fo…
Real multiplication through explicit correspondences
Abhinav Kumar, Ronen E. Mukamel
We compute equations for real multiplication on the divisor classes of genus two curves via algebraic correspondences. We do so by implementing van Wamelen's method for computing e…
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…
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…
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…