1 citations · 3 across the 11 of their papers we have counts for
11 papers
Algorithms for hyperelliptic Mumford Curves -adic Uniformization, -adic integrals and -adic heights
Enis Kaya, Marc Masdeu, J. Steffen Müller +1
Mumford curves generalize the Tate uniformization of elliptic curves with split multiplicative reduction and provide p-adic analogues of the uniformization of Riemann surfaces. In…
Inverse curve problems on del Pezzo surfaces
Enis Kaya, Stephen McKean, Sam Streeter +1
We classify the number of -rational lines and conic fibrations on del Pezzo surfaces over a field in terms of relatively minimal surfaces and establish rational curve analog…
Algorithms for -adic Heights on Hyperelliptic Curves of Arbitrary Reduction
Francesca Bianchi, Enis Kaya, J. Steffen Müller
In this paper, we develop an algorithm for computing Coleman--Gross (and hence Nekovář) -adic heights on hyperelliptic curves over number fields with arbitrary reduction type ab…
Coleman-Gross Heights and -adic Néron Functions on Jacobians of Genus Curves
Francesca Bianchi, Enis Kaya, J. Steffen Müller
We develop a theory of -adic Néron functions on abelian varieties, depending on various auxiliary choices, and show that the global -adic height functions constructed by Mazu…
Jumps of Jacobians via orthogonal canonical forms
Enis Kaya, Michaël Maex, Art Waeterschoot
Given a smooth, proper curve over a discretely valued field , we equip the -vector space with a canonical discrete valuation which m…
Computation of Admissible Arakelov-Green Functions on Metrized Graphs
Ruben Merlijn van Dijk, Enis Kaya
Metrized graphs are nonarchimedean analogues of Riemann surfaces, and Arakelov-Green functions on these graphs are of fundamental importance for some aspects of arithmetic geometry…
Sampling from -adic algebraic manifolds
Yassine El Maazouz, Enis Kaya
We present a method for sampling points from an algebraic manifold, either affine or projective, defined over a local field, with a prescribed probability distribution. Inspired by…
Tropical invariants for binary quintics and reduction types of Picard curves
Paul Alexander Helminck, Yassine El Maazouz, Enis Kaya
We express the reduction types of Picard curves in terms of tropical invariants associated to binary quintics. We also give a general framework for tropical invariants associated t…
Lines on -adic and real cubic surfaces
Rida Ait El Manssour, Yassine El Maazouz, Enis Kaya +1
We study lines on smooth cubic surfaces over the field of -adic numbers, from a theoretical and computational point of view. Segre showed that the possible counts of such lines…
Explicit Vologodsky Integration for Hyperelliptic Curves
Enis Kaya
Vologodsky's theory of -adic integration plays a central role in computing several interesting invariants in arithmetic geometry. In contrast with the theory developed by Colema…
p-adic integration on bad reduction hyperelliptic curves
Eric Katz, Enis Kaya
In this paper, we introduce an algorithm for computing p-adic integrals on bad reduction hyperelliptic curves. For bad reduction curves, there are two notions of p-adic integration…