The class of the locus of intermediate Jacobians of cubic threefolds

We study the locus of intermediate Jacobians of cubic threefolds within the moduli space of complex principally polarized abelian fivefolds, and its generalization to arbitrary genus - the locus of abelian varieties with a singular odd two-torsion point on the theta divisor. Assuming that this locus has expected codimension (which we show to be true for genus up to 5), we compute the class of this locus, and of is closure in the perfect cone toroidal compactification, in the Chow, homology, and the tautological ring. We work out the cases of genus up to 5 in detail, obtaining explicit expressions for the classes of the closures of the locus of products of an elliptic curve and a hyperelliptic genus 3 curve, in moduli of principally polarized abelian fourfolds, and of the locus of intermediate Jacobians in genus 5. In the course of our computation we also deal with various intersections of boundary divisors of a level toroidal compactification, which is of independent interest in understanding the cohomology and Chow rings of the moduli spaces.Comment: v2: new section 9 on the geometry of the boundary of the locus of intermediate Jacobians of cubic threefolds. Final version to appear in Invent. Mat

Deformation of canonical morphisms and the moduli of surfaces of general type

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different $c_1^2$ and $\chi$. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces $\mathcal M_{(x',0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.Comment: 32 pages. Final version with some simplifications and clarifications in the exposition. To appear in Invent. Math. (the final publication is available at springerlink.com

The Curve of Compactified 6D Gauge Theories and Integrable Systems

We analyze the Seiberg-Witten curve of the six-dimensional N=(1,1) gauge theory compactified on a torus to four dimensions. The effective theory in four dimensions is a deformation of the N=2* theory. The curve is naturally holomorphically embedding in a slanted four-torus--actually an abelian surface--a set-up that is natural in Witten's M-theory construction of N=2 theories. We then show that the curve can be interpreted as the spectral curve of an integrable system which generalizes the N-body elliptic Calogero-Moser and Ruijsenaars-Schneider systems in that both the positions and momenta take values in compact spaces. It turns out that the resulting system is not simply doubly elliptic, rather the positions and momenta, as two-vectors, take values in the ambient abelian surface. We analyze the two-body system in some detail. The system we uncover provides a concrete realization of a Beauville-Mukai system based on an abelian surface rather than a K3 surface.Comment: 22 pages, JHEP3, 4 figures, improved readility of figures, added reference

The spectrum of BPS branes on a noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to C^3/Z_3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.Comment: harvmac, 45 pp. (v2: added references

F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds

The Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X contains information about the abelian sector of the six-dimensional theory obtained by compactifying F-theory on X. After examining features of the abelian anomaly coefficient matrix and U(1) charge quantization conditions of general F-theory vacua, we study Calabi-Yau threefolds with Mordell-Weil rank-one as a first step towards understanding the features of the Mordell-Weil group of threefolds in more detail. In particular, we generate an interesting class of F-theory models with U(1) gauge symmetry that have matter with both charges 1 and 2. The anomaly equations --- which relate the Neron-Tate height of a section to intersection numbers between the section and fibral rational curves of the manifold --- serve as an important tool in our analysis.Comment: 29 pages + appendices, 5 figures; v2: minor correction

Quantum algorithms for algebraic problems

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor.Comment: 52 pages, 3 figures, to appear in Reviews of Modern Physic

The CMS Phase-1 pixel detector upgrade

The CMS detector at the CERN LHC features a silicon pixel detector as its innermost subdetector. The original CMS pixel detector has been replaced with an upgraded pixel system (CMS Phase-1 pixel detector) in the extended year-end technical stop of the LHC in 2016/2017. The upgraded CMS pixel detector is designed to cope with the higher instantaneous luminosities that have been achieved by the LHC after the upgrades to the accelerator during the first long shutdown in 2013–2014. Compared to the original pixel detector, the upgraded detector has a better tracking performance and lower mass with four barrel layers and three endcap disks on each side to provide hit coverage up to an absolute value of pseudorapidity of 2.5. This paper describes the design and construction of the CMS Phase-1 pixel detector as well as its performance from commissioning to early operation in collision data-taking.Peer reviewe