New formulas for Faltings delta invariant
Robert Wilms (Bonn)
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When 
Jan 28, 2016 from 02:15 pm to 03:00 pm 
Where  Mainz, 05432 (Hilbertraum) 
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Abstract: In this talk we will give new formulas for Faltings delta invariant of Riemann surfaces. This invariant plays a crucial role in Arakelov theory of arithmetic surfaces, where it appears in the arithmetic Noether formula. We will deduce a lot of applications, for example, a lower bound of the delta invariant only in terms of the genus, a canonical extension of the delta invariant to abelian varieties, an improved version of Szpiro's small points conjecture for cycle covers, a bound of the Arakelov heights of Weierstraß points in terms of the Faltings height and a bound of the ArakelovGreen function in terms of the delta invariant. In the case of hyperelliptic curves we will also obtain an arithmetic analogous of the BogomolovMiyaokaYau inequality and an effective version of the Bogomolov conjecture.