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 development is especially corresponding to Hirzebruch-Zagier cycles. those new items are analyzed intimately and their major houses are defined. specifically, the amount of twisted Teichmüller curves is calculated and their elements are partly categorized. The research of algebraic curves on Hilbert modular surfaces has been broadly lined within the literature as a result of their mathematics value. between those, twisted diagonals (Hirzebruch-Zagier cycles) are probably the most very important examples.
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