A Pair of Rigid Surfaces with pg= q = 2 and K2= 8 Whose Universal Cover is Not the Bidisk

We construct two complex-conjugated rigid minimal surfaces with pg = q = 2 and K2 = 8 whose universal cover is not biholomorphic to the bidisk H × H. We show that these are the unique surfaces with these invariants and Albanese map of degree 2, apart from the family of product-quotient surfaces given in [33]. This completes the classification of surfaces with pg = q = 2, K2 = 8, and Albanese map of degree 2

Negative curves on algebraic surfaces

We study curves of negative self-intersection on algebraic surfaces. We obtain results for smooth complex projective surfaces X on the number of reduced, irreducible curves C of negative self-intersection C^2. The only known examples of surfaces for which C^2 is not bounded below are in positive characteristic, and the general expectation is that no examples can arise over the complex numbers. Indeed, we show that the idea underlying the examples in positive characteristic cannot produce examples over the complex number field. The previous version of this paper claimed to give a counterexample to the Bounded Negativity Conjecture. The idea of the counterexample was to use Hecke translates of a smooth Shimura curve in order to create an infinite sequence of curves violating the Bounded Negativity Conjecture. To this end we applied Hirzebruch Proportionality to all Hecke translates, simultaneously desingularized by a version of Jaffee's Lemma which exists in the literature but which turns out to be false. Indeed, in the new version of the paper, we show that only finitely many Hecke translates of a special subvariety of a Hilbert modular surface remain smooth. This new result is based on work done jointly with Xavier Roulleau, who has been added as an author. The other results in the original posting of this paper remain unchanged.Comment: 14 pages, X. Roulleau added as author, counterexample to Bounded Negativity Conjecture withdrawn and replaced by a proof that there are only finitely many smooth Shimura curves on a compact Hilbert modular surface; the other results in the original posting of this paper remain unchange

How do edge states position themselves in a quantum Hall graphene pn junction?

Recent experiments have shown that electronic Mach-Zehnder interferometers of unprecedented fidelities could be built using a graphene pn junction in the quantum Hall regime. In these junctions, two different edge states corresponding to two different valley configurations are spatially separated and form the two arms of the interferometer. The observed separation, of several tens of nanometers, has been found to be abnormally high and thus associated to unrealistic values of the exchange interaction. In this work, we show that, although the separation is due to exchange interaction, its actual value is entirely governed by the sample geometry and independent of the value of the exchange splitting. Our analysis follows the lines of the classical work of Chklovski-Shklovskii- Glazman on electrostatically induced edge state reconstruction and includes quantitative numerical calculations in the experimental geometries.Comment: 4 pages, 4 figure

Non-Equilibrium Edge Channel Spectroscopy in the Integer Quantum Hall Regime

Heat transport has large potentialities to unveil new physics in mesoscopic systems. A striking illustration is the integer quantum Hall regime, where the robustness of Hall currents limits information accessible from charge transport. Consequently, the gapless edge excitations are incompletely understood. The effective edge states theory describes them as prototypal one-dimensional chiral fermions - a simple picture that explains a large body of observations and calls for quantum information experiments with quantum point contacts in the role of beam splitters. However, it is in ostensible disagreement with the prevailing theoretical framework that predicts, in most situations, additional gapless edge modes. Here, we present a setup which gives access to the energy distribution, and consequently to the energy current, in an edge channel brought out-of-equilibrium. This provides a stringent test of whether the additional states capture part of the injected energy. Our results show it is not the case and thereby demonstrate regarding energy transport, the quantum optics analogy of quantum point contacts and beam splitters. Beyond the quantum Hall regime, this novel spectroscopy technique opens a new window for heat transport and out-of-equilibrium experiments.Comment: 13 pages including supplementary information, Nature Physics in prin

On Fano schemes of complete intersections

We provide enumerative formulas for the degrees of varieties parameterizing hypersurfaces and complete intersections which contain pro-jective subspaces and conics. Besides, we find all cases where the Fano scheme of the general complete intersection is irregular of dimension at least 2, and for the Fano surfaces we deduce formulas for their holomorphic Euler characteristic.Comment: Added lacking references, corrected acknowledgments, minor editorial change

Structural and Electrical Characterization of Bi2Se3 Nanostructures Grown by Metalorganic Chemical Vapor Deposition

We characterize nanostructures of Bi2Se3 that are grown via metalorganic chemical vapor deposition using the precursors diethyl selenium and trimethyl bismuth. By adjusting growth parameters, we obtain either single-crystalline ribbons up to 10 microns long or thin micron-sized platelets. Four-terminal resistance measurements yield a sample resistivity of 4 mOhm-cm. We observe weak anti-localization and extract a phase coherence length l_phi = 178 nm and spin-orbit length l_so = 93 nm at T = 0.29 K. Our results are consistent with previous measurements on exfoliated samples and samples grown via physical vapor deposition.Comment: Related papers at http://pettagroup.princeton.ed

Quotients of Fano surfaces

Fano surfaces parametrize the lines of smooth cubic threefolds. In this paper, we study their quotients by some of their automorphism sub-groups. We obtain in that way some interesting surfaces of general type.Comment: 21 pages, corrections according to the referee request, to appear in Rendiconti Lince

On finiteness of curves with high canonical degree on a surface

Abstract. The canonical degree of a curve C on a surface X is KX ·C. Our main result, Theorem 1.1, is that on a surface of general type there are only finitely many curves with negative self–intersection and sufficiently large canonical degree. Our proof strongly relies on results by Miyaoka. We extend our result both to surfaces not of general type and to non–negative curves, and give applications, e.g. to finiteness of negative curves on a general blow–up of P2 at n ≥ 10 general points (a result related to Nagata’s Conjecture). We finally discuss a conjecture by Vojta concerning the asymptotic behaviour of the ratio between the canonical degree and the geometric genus of a curve varying on a surface. The results in this paper go in the direction of understanding the bounded negativity problem. 1. Introduction. Let C be a projective curve on a smooth projective complex surface X. By curve we mean an irreducible, reduced 1–dimensional scheme. We denote by g = g(C) its geometric genus and by p = pa(C) its arithmetic genus, i.e. C2 +K ·C = 2pa − 2, where K = KX is a canonical divisor of X. We set δ = δ(C) = p − g. We call a curve negative if C2 < 0. The canonical degree of C is kC = K · C, often simply denoted by k. If g(C) 6 = 1