By Christian Weiß
Those notes introduce a brand new category of algebraic curves on Hilbert modular surfaces. those curves are known as twisted Teichmüller curves, simply because their building is especially corresponding to Hirzebruch-Zagier cycles. those new items are analyzed intimately and their major homes are defined. particularly, the amount of twisted Teichmüller curves is calculated and their elements are partly categorized. The learn of algebraic curves on Hilbert modular surfaces has been broadly lined within the literature as a result of their mathematics significance. between those, twisted diagonals (Hirzebruch-Zagier cycles) are essentially the most very important examples.
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