Arakelov inequalities in higher dimensions

Author:

Kovács Sándor J.1,Taji Behrouz2

Affiliation:

1. Department of Mathematics , University of Washington , Box 354350 , Seattle , Washington, 98195 , USA

2. School of Mathematics and Statistics , The University of New South Wales , Sydney , NSW 2052 Australia

Abstract

Abstract We develop a Hodge theoretic invariant for families of projective manifolds that measures the potential failure of an Arakelov-type inequality in higher dimensions, one that naturally generalizes the classical Arakelov inequality over regular quasi-projective curves. We show that, for families of manifolds with ample canonical bundle, this invariant is uniformly bounded. As a consequence, we establish that such families over a base of arbitrary dimension satisfy the aforementioned Arakelov inequality, answering a question of Viehweg.

Funder

National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference62 articles.

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3. S. J. Arakelov, Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 1269–1293.

4. E. Bedulev and E. Viehweg, On the Shafarevich conjecture for surfaces of general type over function fields, Invent. Math. 139 (2000), no. 3, 603–615.

5. B. Bhatt, W. Ho, Z. Patakfalvi and C. Schnell, Moduli of products of stable varieties, Compos. Math. 149 (2013), no. 12, 2036–2070.

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