Toric degenerations of rational curves of degree n+2 in P^n

Author: 
Date created: 
2020-08-11
Identifier: 
etd20995
Keywords: 
Toric degeneration
Rational curves
Khovanskii-finite valuation
Abstract: 

A common technique for studying a projective variety relies on finding a flat degeneration to a toric variety, which is a variety described by combinatorial data. However, it is not clear in general how to find such a degeneration or even if one exists. Ilten and Wrobel have shown that a very general rational plane curve of degree at least four does not admit this degeneration. In this thesis, we investigate the existence of toric degenerations for the special case of projective rational curves of degree n+2 in P^n where n≥3. Using work of Buczyński, Ilten, and Ventura, we obtain explicit parametrizations for all rational curves of degree n+2 in P^n and characterize which of these admit such a degeneration. Our results show that for these curves, the problem of having a toric degeneration can be decided algorithmically.

Document type: 
Thesis
Rights: 
This thesis may be printed or downloaded for non-commercial research and scholarly purposes. Copyright remains with the author.
File(s): 
Supervisor(s): 
Nathan Ilten
Department: 
Science: Department of Mathematics
Thesis type: 
(Thesis) M.Sc.
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