By Christian Weiß

Those notes introduce a brand new type of algebraic curves on Hilbert modular surfaces. those curves are known as twisted Teichmüller curves, simply because their building is particularly comparable to Hirzebruch-Zagier cycles. those new gadgets are analyzed intimately and their major homes are defined. specifically, the amount of twisted Teichmüller curves is calculated and their elements are in part categorized. The learn of algebraic curves on Hilbert modular surfaces has been extensively lined within the literature as a result of their mathematics significance. between those, twisted diagonals (Hirzebruch-Zagier cycles) are probably the most very important examples.

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