8 citations · 15 across the 10 of their papers we have counts for
10 papers · 1 filter
On (2,2)-decomposable genus 4 Jacobians
Nils Bruin, Avinash Kulkarni
We consider the question of when a Jacobian of a curve of genus admits a -isogeny to two polarized dimension abelian varieties. We find that one of them must be a J…
A census of cubic fourfolds over
Asher Auel, Avinash Kulkarni, Jack Petok +1
We compute a complete set of isomorphism classes of cubic fourfolds over . Using this, we are able to compile statistics about various invariants of cubic fourfolds,…
A database of basic numerical invariants of Hilbert modular surfaces
Eran Assaf, Angelica Babei, Ben Breen +8
We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.
Nonarchimedean integral geometry
Peter Bürgisser, Avinash Kulkarni, Antonio Lerario
Let be a nonarchimedean local field of characteristic zero with valuation ring , for instance, and . We prove a general integral geometric f…
On intersections of symmetric determinantal varieties and theta characteristics of canonical curves
Avinash Kulkarni, Sameera Vemulapalli
From a block-diagonal tensor symmetric in the last two entries one obtains two varieties: an intersection of symmetric determinantal hypersurfaces…
On the eigenpoints of cubic surfaces
Türkü Özlüm Celik, Francesco Galuppi, Avinash Kulkarni +1
We show that the eigenschemes of symmetric tensors are parametrized by a linear subvariety of the Grassmannian . We also…
-adic Integral Geometry
Avinash Kulkarni, Antonio Lerario
We prove a -adic version of the Integral Geometry Formula for averaging the intersection of two -adic projective algebraic sets. We apply this result to give bounds on the nu…
Tritangents and Their Space Sextics
Turku Ozlum Celik, Avinash Kulkarni, Yue Ren +1
Two classical results in algebraic geometry are that the branch curve of a del Pezzo surface of degree 1 can be embedded as a space sextic curve and that every space sextic curve h…
Certifying reality of projections
Jonathan Hauenstein, Avinash Kulkarni, Emre Can Sertöz +1
Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., s…
Real Space Sextics and their Tritangents
Avinash Kulkarni, Yue Ren, Mahsa Sayyary Namin +1
The intersection of a quadric and a cubic surface in 3-space is a canonical curve of genus 4. It has 120 complex tritangent planes. We present algorithms for computing real tritang…