Linear Toric Fibrations

Rocco, Sandra Di

doi:10.1007/978-3-319-04870-3_4

Lecture Notes in Mathematics

2014

DOI: 10.1007/978-3-319-04870-3_4

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Linear Toric Fibrations

Sandra Di Rocco

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Cited by 3 publications

References 31 publications

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Distortion Varieties

et al. 2017

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The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter distortions. These are based on Chow polytopes and Gröbner bases. Multi-parameter distortions are studied using tropical geometry. The motivation for distortion varieties comes from multi-view geometry in computer vision. Our theory furnishes a new framework for formulating and solving minimal problems for camera models with image distortion.

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Distortion Varieties

et al. 2017

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Local positivity of line bundles on smooth toric varieties and Cayley polytopes

Lundman

2016

Journal of Symbolic Computation

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For any non-negative integer k the k-th osculating dimension at a given point x of a variety X embedded in projective space gives a measure of the local positivity of order k at that point. In this paper we show that a smooth toric embedding having maximal k-th osculating dimension, but not maximal (k + 1)-th osculating dimension, at every point is associated to a Cayley polytope of order k. This result generalises an earlier characterisation by David Perkinson. In addition we prove that the above assumptions are equivalent to requiring that the Seshadri constant is exactly k at every point of X, generalising a result of Atsushi Ito.The author is supported by the V.R. grant NT:2010-5563. arXiv:1307

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Bounds on the Picard rank of toric Fano varieties with minimal curve constraints

Beheshti

Wormleighton

2023

Proc. Amer. Math. Soc.

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We study the Picard rank of smooth toric Fano varieties constrained to possess families of minimal rational curves of given degree. We discuss variants of a conjecture of Chen–Fu–Hwang and prove a version of their statement that recovers the original conjecture in sufficiently high dimension. We also prove new cases of the original conjecture for high degrees in all dimensions. Our main tools come from toric Mori theory and the combinatorics of Fano polytopes.

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Linear Toric Fibrations

Cited by 3 publications

References 31 publications

Distortion Varieties

Distortion Varieties

Local positivity of line bundles on smooth toric varieties and Cayley polytopes

Bounds on the Picard rank of toric Fano varieties with minimal curve constraints

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