Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte

Coset Constructions in Chern-Simons Gauge Theory

Coset constructions in the framework of Chern-Simons topological gauge theories are studied. Two examples are considered: models of the types ${U(1)_p\times U(1)_q\over U(1)_{p+q}}\cong U(1)_{pq(p+q)}$ with $p$ and $q$ coprime integers, and ${SU(2)_m\times SU(2)_1\over SU(2)_{m+1}}$. In the latter case it is shown that the Chern-Simons wave functionals can be identified with t he characters of the minimal unitary models, and an explicit representation of the knot (Verlinde) operators acting on the space of $c<1$ characters is obtained.Comment: 15 page

BRST Quantization of String Theory in AdS(3)

We study the BRST quantization of bosonic and NSR strings propagating in AdS(3) x N backgrounds. The no-ghost theorem is proved using the Frenkel-Garland-Zuckerman method. Regular and spectrally-flowed representations of affine SL(2,R) appear on an equal footing. Possible generalizations to related curved backgrounds are discussed.Comment: JHEP style, 23 pages; v2:minor changes and references added; v3: typos corrected, version to appear in JHEP; v4: one reference adde

Polynomials for Torus Links from Chern-Simons Gauge Theories

Invariant polynomials for torus links are obtained in the framework of the Chern-Simons topological gauge theory. The polynomials are computed as vacuum expectation values on the three-sphere of Wilson line operators representing the Verlinde algebra of the corresponding rational conformal field theory. In the case of the $SU(2)$ gauge theory our results provide explicit expressions for the Jones polynomial as well as for the polynomials associated to the $N$-state ($N>2$) vertex models (Akutsu-Wadati polynomials). By means of the Chern-Simons coset construction, the minimal unitary models are analyzed, showing that the corresponding link invariants factorize into two $SU(2)$ polynomials. A method to obtain skein rules from the Chern-Simons knot operators is developed. This procedure yields the eigenvalues of the braiding matrix of the corresponding conformal field theory.Comment: 50 page

Ranks of tensors and a generalization of secant varieties

We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \otimes C^b \otimes C^b. We review the literature from a geometric perspective.Comment: 22 pages; final published version; Linear Algebra and its Applications 201

On the Quantum Invariant for the Spherical Seifert Manifold

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to $\Gamma$.Comment: 36 page

ADHM Construction of Instantons on the Torus

We apply the ADHM instanton construction to SU(2) gauge theory on T^n x R^(4-n)for n=1,2,3,4. To do this we regard instantons on T^n x R^(4-n) as periodic (modulo gauge transformations) instantons on R^4. Since the R^4 topological charge of such instantons is infinite the ADHM algebra takes place on an infinite dimensional linear space. The ADHM matrix M is related to a Weyl operator (with a self-dual background) on the dual torus tilde T^n. We construct the Weyl operator corresponding to the one-instantons on T^n x R^(4-n). In order to derive the self-dual potential on T^n x R^(4-n) it is necessary to solve a specific Weyl equation. This is a variant of the Nahm transformation. In the case n=2 (i.e. T^2 x R^2) we essentially have an Aharonov Bohm problem on tilde T^2. In the one-instanton sector we find that the scale parameter, lambda, is bounded above, (lambda)^2 tv<4 pi, tv being the volume of the dual torus tilde T^2.Comment: 35 pages, LATeX. New section on Nahm transform included, presentation improved, reference added, to appear in Nuclear Physics

Is Area-Wide Pest Management Useful? The Case of Citrus Greening.

Citrus greening currently poses a severe threat to citrus production worldwide. No treatment or management strategy is yet available to cure the disease. Scientists recommend controlling the vector of the disease, and area-wide pest management has been proposed as a superior alternative to individual pest management. We analyzed a unique dataset of farm-level citrus yields that allowed us to test this hypothesis. We found that yields of blocks located in an area with higher participation in coordinated sprays were 28%, 73% and 98% percent higher in 2012/13, 2013/14, and 2014/15, respectively, compared to the yields of blocks under the same management but located in an area with lower participation; providing evidence on the efficiency of a well-performing pest management area to deal with HLB. However, participation in CHMAs has not been commensurate with this evidence. We present survey data that provide insights about producers’ preferences and attitudes toward the area-wide pest management program. Despite the economic benefit we found area-wide pest management can provide, the strategic uncertainty involved in relying on neighbors seems to impose too high of a cost for most growers, who end up not coordinating sprays

A Historiometric Examination of Machiavellianism and a New Taxonomy of Leadership

Although researchers have extensively examined the relationship between charismatic leadership and Machiavellianism (Deluga, 2001; Gardner & Avolio, 1995; House & Howell, 1992), there has been a lack of investigation of Machiavellianism in relation to alternative forms of outstanding leadership. Thus, the purpose of this investigation was to examine the relationship between Machiavellianism and a new taxonomy of outstanding leadership comprised of charismatic, ideological, and pragmatic leaders. Using an historiometric approach, raters assessed Machiavellianism via the communications of 120 outstanding leaders in organizations across the domains of business, political, military, and religious institutions. Academic biographies were used to assess twelve general performance measures as well as twelve general controls and five communication specific controls. The results indicated that differing levels of Machiavellianism is evidenced across the differing leader types as well as differing leader orientation. Additionally, Machiavellianism appears negatively related to performance, though less so when type and orientation are taken into account.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline