Faltings height and Néron–Tate height of a theta divisor

Faltings Modular Height and Self-intersection of Dualizing Sheaf

is finite under the following equivalence (cf. Theorem 3.1). For stable curves X and Y over OK , X is equivalent to Y if X ⊗OK OK′ ≃ Y ⊗OK OK′ for some finite extension field K ′ of K. In §1, we will consider semistability of the kernel of H(C,L) ⊗ OC → L, which gives a generalization of [PR]. In §2, an inequality of self-intersection and height will be treated. Finally, §3 is devoted to finite...

Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height

In this paper, we prove an explicit arithmetic intersection formula between arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles in a Hilbert modular surface over Z. As applications, we obtain the first ‘non-abelian’ Chowla-Selberg formula, which is a special case of Colmez’s conjecture; an explicit arithmetic intersection formula between arithmetic Humbert surfaces and CM cycles in t...

A diallel analysis of height in wheat

The Theta Divisor and Three-manifold Invariants

In this paper we study an invariant for oriented three-manifolds with b1 > 0, which is defined using Heegaard splittings and the theta divisor of a Riemann surface. The paper is divided into two parts, the first of which gives the definition of the invariant, and the second of which identifies it with more classical (torsion) invariants of three-manifolds. Its close relationship with Seiberg-Wi...

A Survey on Current Methods of Carpal Height Ratio Measurement and Suggestion of a New Method

Background & Aims: Two famous methods are commonly used for the measurement of carpal height ratio. Both methods are performed on anteroposterior radiogram and have some shortcomings. We are going to introduce a new method for measuring this index in lateral view of the wrist radiogram' Methods: This cross-sectional and case-control study was conducted on 100 anteroposterior and lateral radiogr...