Michele Ancona

Metric and spectral aspects of random complex divisors

For any integer n\geq 2 , we prove that for any large enough integer d , with large probability the injectivity radius of a random degree d complex hypersurface in \mathbb{C}P^{n} is larger than {d^{-(n+2)/2}} . Here the hypersurface is endowed with the restriction of the ambient...