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The birational geometry of tropical compactifications

Colin Diemer

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Abstract

I would like thank my advisor Antonella Grassi for suggesting tropical geometry as a possible dissertation topic (and for her truly commendable patience and willingness to help). Ron Donagi, Tony Pantev, Jonathan Block, and Erik van Erp also helped me find my way mathematically here at Penn. Conversations with Paul Hacking, Jenia Tevelev, Eric Katz, Ilia Zharkov, Eduardo Cattani, and Alicia Dickenstein were beneficial during the preparation of this thesis. This thesis is dedicated to my father. ii

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I would like thank my advisor Antonella Grassi for suggesting tropical geometry as a possible dissertation topic (and for her truly commendable patience and willingness to help). Ron Donagi, Tony Pantev, Jonathan Block, and Erik van Erp also helped me find my way mathematically here at Penn. Conversations with Paul Hacking, Jenia Tevelev, Eric Katz, Ilia Zharkov, Eduardo Cattani, and Alicia Dickenstein were beneficial during the preparation of this thesis. This thesis is dedicated to my father. ii

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Available abstract

I would like thank my advisor Antonella Grassi for suggesting tropical geometry as a possible dissertation topic (and for her truly commendable patience and willingness to help). Ron Donagi, Tony Pantev, Jonathan Block, and Erik van Erp also helped me find my way mathematically here at Penn. Conversations with Paul Hacking, Jenia Tevelev, Eric Katz, Ilia Zharkov, Eduardo Cattani, and Alicia Dickenstein were beneficial during the preparation of this thesis. This thesis is dedicated to my father. ii

Key concepts: Tropical geometry, Mathematics, Compactification (mathematics), Birational geometry, Morphism, Geometry, Algebraic geometry, Pure mathematics

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