Let S be a surface in P2 × P2 given by the intersection of a (1,1)form and a (2,2)-form. Then S is a K3 surface with two noncommuting involutions σx and σy . In 1991 the second author constructed two height functions ĥ+ and ĥ− which behave canonically with respect to σx and σy , and in 1993 together with the first author showed in general how to decompose such canonical heights into a sum of lo...

Let E D .E; h/ be a hermitian vector bundle over Spec.OK /; for some number field K . The main result of this paper shows that if X is a K 3 surface with Picard group of rank 1 and embedded in P.E/; then its Faltings height is bounded below in terms of the Arakelov degree of E; the first and the last minima of Zhang. This inequality is stronger than the one given by the semistability of the Hil...

We construct Adams operations on higher algebraic K-groups induced by operations such as symmetric powers on any suitable exact category, by constructing an explicit map of spaces, combinatorially deened. The map uses the S-construction of Waldhausen, and deloops (once) earlier constructions of the map.

We show that certain classes of K3 bered Calabi-Yau manifolds derive from orbifolds of global products of K3 surfaces and particular types of curves. This observation explains why the gauge groups of the heterotic duals are determined by the structure of a single K3 surface and provides the dual heterotic picture of conifold transitions between K3 brations. Abstracting our construction from the...

In [4], we have proved the necessary condition for sigraphs on union of k copies cycles of length three with one vertex in common denoted by C 3 to be graceful and sufficiency part of the theorem was discussed in certain special cases when all rim edges are negative and form a maximum matching. In this paper, we discuss the sufficiency part of the theorem on gracefulness of sigraphs on C 3 part...

We show that the geometry of K3 surfaces with singularities of type AD -E contains enough information to reconstruct a copy of the Lie algebra associated to the given Dynkin diagram. We apply this construction to explain the enhancement of symmetry in F and IIA theories compactified on singular K3's.

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kähler parameters. We show that Kähler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-parameter family of K3 surfaces constructed as blow-ups of the T /Z2 orbifold with ma...

Top-down partitioning has focused on minimum cut or ratio cut objectives, while bottom-up clustering has focused on density-based objectives. In seeking a more uni ed perspective, we propose a new sum of densities measure for multi-way circuit decomposition, where the density of a subhypergraph is the ratio of the number of edges to the number of nodes in the subhypergraph. Finding a k-way part...

We introduce an invariant of the hyperbolic 3-manifolds which appears in the K-theory of certain C*-algebras. Namely, such an invariant is essentially an algebraic number field K with a fixed equivalence class of ideals in the ring of integers of K. The C*-algebras in question are the crossed product C*-algebras attached to the monodromy transformation of the 3-manifolds which fiber over the ci...