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arXiv · 1407.6561

On the equidistribution of totally geodesic submanifolds in compact locally symmetric spaces and application to boundedness results for negative curves and exceptional divisors

Vincent Koziarz·Julien Maubon
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Abstract

We prove an equidistribution result for totally geodesic submanifolds in a compact locally symmetric space. In the case of Hermitian locally symmetric spaces, this gives a convergence theorem for currents of integration along totally geodesic subvarieties. As a corollary, we obtain that on a complex surface which is a compact quotient of the bidisc or of the 2-ball, there is at most a finite number of totally geodesic curves with negative self intersection. More generally, we prove that there are only finitely many exceptional totally geodesic divisors in a compact Hermitian locally symmetric space of the noncompact type of dimension at least 2.

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Vincent Koziarz, Julien Maubon. 2015-11-06. On the equidistribution of totally geodesic submanifolds in compact locally symmetric spaces and application to boundedness results for negative curves and exceptional divisors. https://arxiv.org/abs/1407.6561

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