Frizzell, Carrie R.2018-04-232018-04-232018-05-01http://hdl.handle.net/2097/38898When considering an unramified double cover π : C’→ C of nonsingular algebraic curves, the Prym variety (P; θ) of the cover arises from the sheet exchange involution of C’ via extension to the Jacobian J(C’). The Prym is defined to be the anti-invariant (odd) part of this induced map on J(C’), and it carries twice a principal polarization of J(C’). The pair (P; θ), where θ is a representative of a theta divisor of J(C’) on P, makes the Prym a candidate for the Jacobian of another curve. In 1974, David Mumford proved that for an unramified double cover π : C’η →C of a plane quintic curve, where η is a point of order two in J(C), then the Prym (P; θ) is not a Jacobian if the theta characteristic L(η) is odd, L the hyperplane section. We sought to find an analog of Mumford's result in the tropical geometry setting. We consider the Prym variety of certain unramified double covers of three types of tropical plane quintics. Applying the theory of lattice dicings, which give affine invariants of the Prym lattice, we found that when the parity α(H₃) is even, H₃ the cycle associated to the hyperplane section and the analog to η in the classical setting, then the Prym is not a Jacobian, and is a Jacobian when the parity is odd.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/Lattice dicingPrym varietiesUnramified double coversJacobianTropical curvesTropical geometryThesis