In this paper we consider the question of determining the geometric genera of irreducible curves lying on a very general surface S of degree d > 5 in P (the cases d 6 4 are well known). For any d > 4 we introduce the set Gaps(d) of all non–negative integers which are not realized as geometric genera of irreducible curves on a very general surface of degree d in P. We prove that Gaps(d) is finit...

We show that an unification of quantum mechanics and general relativity implies that there is a fundamental length in Nature in the sense that no operational procedure would be able to measure distances shorter than the Planck length. Furthermore we give an explicit realization of an old proposal by Anderson and Finkelstein who argued that a fundamental length in nature implies unimodular gravi...

At Planck-scale, spacetime is " foamy " due to quantum fluctuations predicted by quantum gravity. Here we consider the possibility of using spacetime foam-induced phase incoherence of light from distant galaxies and gamma-ray bursters to probe Planck-scale physics. In particular, we examine the cumulative effects of spacetime fluctuations over a huge distance. Our analysis shows that they are f...

We study the Planck scale effects on Jarlskog determiant. Quantum gravitational (Planck scale) effects lead to an effective SU(2) × U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which give rise to additional terms in neutrino mass matrix on electroweak symmetry breaking. We assume that gravitational interaction is flavor blind and compute the Jarlskog determiant due...