Tropical quadrics through three points

Rational Points on Singular Intersections of Quadrics

— Given an intersection of two quadrics X ⊂ Pm−1, with m > 9, the quantitative arithmetic of the set X(Q) is investigated under the assumption that the singular locus of X consists of a pair of conjugate singular points defined over Q(i).

Mapping threefolds onto three-quadrics

We prove that the degree of a nonconstant morphism from a smooth projective 3-fold X with Néron-Severi group Z to a smooth 3-dimensional quadric is bounded in terms of numerical invariants of X. In the special case where X is a 3-dimensional cubic we show that there are no such morphisms. The main tool in the proof is Miyaoka’s bound on the number of double points of a surface.

Integral Points on Quadrics in Three Variables Whose Coordinates Have Few Prime Factors

The projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using uncalibrated cameras

In this paper we present an algorithm for the simultaneous projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using Bundle Adjustment. In contrast, most existing work on projective reconstruction focuses mainly on one type of primitive. Furthermore, for the reconstruction of quadrics (both full-rank and degenerate) and plane conics, a novel algorithm for ...

Tropical Independence Ii: the Maximal Rank Conjecture for Quadrics

Building on our earlier results on tropical independence and shapes of divisors in tropical linear series, we give a tropical proof of the maximal rank conjecture for quadrics. We also prove a tropical analogue of Max Noether’s theorem on quadrics containing a canonically embedded curve, and state a combinatorial conjecture about tropical independence on chains of loops that implies the maximal...