22 citations · 51 across the 22 of their papers we have counts for
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On arithmetic inequalities for points of bounded degree
Nathan Grieve
We study algebraic points of bounded degree on polarized projective varieties. To do so, we refine further the filtration construction and Subspace Theorem approach, for the study…
Generalized GCD for toric Fano varieties
Nathan Grieve
We study the greatest common divisor problem for torus invariant blowing-up morphisms of nonsingular toric Fano varieties. Our main result applies the theory of Okounkov bodies tog…
On Duistermaat-Heckman measure for filtered linear series
Nathan Grieve
We revisit work of S. Boucksom, C. Favre, and M. Jonsson (J. Algebraic Geom. \textbf{18} (2009), no. 2, 279--308); Boucksom and H. Chen (Compos. Math. \textbf{147} (2011), no. 4, 1…
Greatest common divisors with moving targets and consequences for linear recurrence sequences
Nathan Grieve, Julie Tzu-Yueh Wang
We establish consequences of the moving form of Schmidt's Subspace Theorem. Indeed, we obtain inequalities that bound the logarithmic greatest common divisor of moving multivariabl…
Divisorial instability and Vojta's Main Conjecture for -Fano varieties
Nathan Grieve
We study Diophantine arithmetic properties of birational divisors in conjunction with concepts that surround -stability for Fano varieties. There is also an interpretat…