scholarly journals Quasimaps to GIT fibre bundles and applications

2021 ◽  
Vol 9 ◽  
Author(s):  
Jeongseok Oh
Keyword(s):  
Moduli Spaces ◽  
Flag Variety ◽  
Fibre Bundles ◽  
Witten Theory ◽  
Do So

Abstract In [4], Brown proved that the I-function of a toric fibration lies on the overruled Lagrangian cone of its $g=0$ Gromov–Witten theory, introduced by Coates and Givental [8]. In this paper, we prove the theorem for partial flag-variety fibrations. To do so, we construct new moduli spaces generalising the idea of Ciocan-Fontanine, Kim and Maulik [7].

scholarly journals Holomorphic anomaly equation for and the Nekrasov-Shatashvili limit of local

2021 ◽  
Vol 9 ◽  
Author(s):  
Pierrick Bousseau ◽  
Honglu Fan ◽  
Shuai Guo ◽  
Longting Wu
Keyword(s):  
Elliptic Curve ◽  
Moduli Spaces ◽  
Topological String ◽  
Holomorphic Anomaly ◽  
Holomorphic Anomaly Equation ◽  
Anomaly Equation ◽  
Witten Theory ◽  
Generating Series ◽  
Maximal Contact ◽  
Higher Genus

Abstract We prove a higher genus version of the genus $0$ local-relative correspondence of van Garrel-Graber-Ruddat: for $(X,D)$ a pair with X a smooth projective variety and D a nef smooth divisor, maximal contact Gromov-Witten theory of $(X,D)$ with $\lambda _g$ -insertion is related to Gromov-Witten theory of the total space of ${\mathcal O}_X(-D)$ and local Gromov-Witten theory of D. Specializing to $(X,D)=(S,E)$ for S a del Pezzo surface or a rational elliptic surface and E a smooth anticanonical divisor, we show that maximal contact Gromov-Witten theory of $(S,E)$ is determined by the Gromov-Witten theory of the Calabi-Yau 3-fold ${\mathcal O}_S(-E)$ and the stationary Gromov-Witten theory of the elliptic curve E. Specializing further to $S={\mathbb P}^2$ , we prove that higher genus generating series of maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ are quasimodular and satisfy a holomorphic anomaly equation. The proof combines the quasimodularity results and the holomorphic anomaly equations previously known for local ${\mathbb P}^2$ and the elliptic curve. Furthermore, using the connection between maximal contact Gromov-Witten invariants of $({\mathbb P}^2,E)$ and Betti numbers of moduli spaces of semistable one-dimensional sheaves on ${\mathbb P}^2$ , we obtain a proof of the quasimodularity and holomorphic anomaly equation predicted in the physics literature for the refined topological string free energy of local ${\mathbb P}^2$ in the Nekrasov-Shatashvili limit.

BPS Monopoles

1997 ◽  
Vol 12 (26) ◽  
pp. 4663-4705 ◽  
Author(s):  
Paul M. Sutcliffe
Keyword(s):  
Moduli Spaces ◽  
Recent Progress ◽  
Witten Theory

We review classical BPS monopoles, their moduli spaces, twistor descriptions and dynamics. Particular emphasis is placed upon symmetric monopoles, where recent progress has been made. Some remarks on the role of monopoles in S duality and Seiberg–Witten theory are also made.

scholarly journals Gromov-Witten theory of root Gerbes I: Structure of genus 0 moduli spaces

2015 ◽  
Vol 99 (1) ◽  
pp. 1-45 ◽  
Author(s):  
Elena Andreini ◽  
Yunfeng Jiang ◽  
Hsian-Hua Tseng
Keyword(s):  
Moduli Spaces ◽  
Witten Theory

scholarly journals A Map Between Moduli Spaces of Connections

2020 ◽  
Author(s):  
Frank Loray ◽  
◽  
Valente Ramírez ◽  
Keyword(s):  
Normal Form ◽  
Elliptic Curve ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Riemann Sphere ◽  
Target Space ◽  
Transformation Rule ◽  
Rank 2 ◽  
Logarithmic Connection ◽  
Do So

We are interested in studying moduli spaces of rank 2 logarithmic connections on elliptic curves having two poles. To do so, we investigate certain logarithmic rank 2 connections defined on the Riemann sphere and a transformation rule to lift such connections to an elliptic curve. The transformation is as follows: given an elliptic curve C with elliptic quotient, and the logarithmic connection, we may pullback the connection to the elliptic curve to obtain a new connection on C. After suitable birational modifications we bring the connection to a particular normal form. The whole transformation is equivariant with respect to bundle automorphisms and therefore defines a map between the corresponding moduli spaces of connections. The aim of this paper is to describe the moduli spaces involved and compute explicit expressions for the above map in the case where the target space is the moduli space of rank 2 logarithmic connections on an elliptic curve C with two simple poles and trivial determinant.

scholarly journals Zero cycles on the moduli space of curves

2020 ◽  
Vol Volume 4 ◽  
Author(s):  
Rahul Pandharipande ◽  
Johannes Schmitt
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Rational Surface ◽  
K3 Surfaces ◽  
Moduli Of Curves ◽  
K3 Surface ◽  
Moduli Space Of Curves ◽  
Moduli Spaces Of Curves ◽  
Open Questions ◽  
Witten Theory

While the Chow groups of 0-dimensional cycles on the moduli spaces of Deligne-Mumford stable pointed curves can be very complicated, the span of the 0-dimensional tautological cycles is always of rank 1. The question of whether a given moduli point [C,p_1,...,p_n] determines a tautological 0-cycle is subtle. Our main results address the question for curves on rational and K3 surfaces. If C is a nonsingular curve on a nonsingular rational surface of positive degree with respect to the anticanonical class, we prove [C,p_1,...,p_n] is tautological if the number of markings does not exceed the virtual dimension in Gromov-Witten theory of the moduli space of stable maps. If C is a nonsingular curve on a K3 surface, we prove [C,p_1,...,p_n] is tautological if the number of markings does not exceed the genus of C and every marking is a Beauville-Voisin point. The latter result provides a connection between the rank 1 tautological 0-cycles on the moduli of curves and the rank 1 tautological 0-cycles on K3 surfaces. Several further results related to tautological 0-cycles on the moduli spaces of curves are proven. Many open questions concerning the moduli points of curves on other surfaces (Abelian, Enriques, general type) are discussed. Comment: Published version

scholarly journals Bott-Samelson Varieties, Subword Complexes and Brick Polytopes

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Laura Escobar
Keyword(s):  
Toric Variety ◽  
Simplicial Complexes ◽  
Flag Variety ◽  
Moment Map ◽  
Coxeter System ◽  
International Audience ◽  
Moment Polytope ◽  
The Moment ◽  
Subword Complex ◽  
Do So

International audience Bott-Samelson varieties factor the flag variety $G/B$ into a product of $\mathbb{C}\mathbb{P}^1$'s with a map into $G/B$. These varieties are mostly studied in the case in which the map into $G/B$ is birational; however in this paper we study fibers of this map when it is not birational. We will see that in some cases this fiber is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to translate this problem into a purely combinatorial one in terms of a subword complex. These simplicial complexes, defined by Knutson and Miller, encode a lot of information about reduced words in a Coxeter system. Pilaud and Stump realized certain subword complexes as the dual to the boundary of a polytope which generalizes the brick polytope defined by Pilaud and Santos. For a nice family of words, the brick polytope is the generalized associahedron realized by Hohlweg and Lange. These stories connect in a nice way: the moment polytope of a fiber of the Bott-Samelson map is the Brick polytope. In particular, we give a nice description of the toric variety of the associahedron.

Holding replication studies to mainstream standards of evidence

2018 ◽  
Vol 41 ◽  
Author(s):  
Duane T. Wegener ◽  
Leandre R. Fabrigar
Keyword(s):  
Replication Studies ◽  
Replication Research ◽  
Standards Of Evidence ◽  
Do So

AbstractReplications can make theoretical contributions, but are unlikely to do so if their findings are open to multiple interpretations (especially violations of psychometric invariance). Thus, just as studies demonstrating novel effects are often expected to empirically evaluate competing explanations, replications should be held to similar standards. Unfortunately, this is rarely done, thereby undermining the value of replication research.

Electron Microscopy of a Herpesvirus Isolated from Marek's Disease in Duck and Chicken Embryo Fibroblast Cultures

1968 ◽  
Vol 26 ◽  
pp. 222-223 ◽  
Author(s):  
Keyvan Nazerian
Keyword(s):  
Inclusion Bodies ◽  
Chicken Embryo Fibroblast ◽  
Marek's Disease ◽  
Marek’S Disease ◽  
Duck Embryo Fibroblast ◽  
Multinucleated Cells ◽  
Viral Particles ◽  
Infected Cells ◽  
And Control ◽  
Do So

A herpes-like virus has been isolated from duck embryo fibroblast (DEF) cultures inoculated with blood from Marek's disease (MD) infected birds. Cultures which contained this virus produced MD in susceptible chickens while virus negative cultures and control cultures failed to do so. This and other circumstantial evidence including similarities in properties of the virus and the MD agent implicate this virus in the etiology of MD.Histochemical studies demonstrated the presence of DNA-staining intranuclear inclusion bodies in polykarocytes in infected cultures. Distinct nucleo-plasmic aggregates were also seen in sections of similar multinucleated cells examined with the electron microscope. These aggregates are probably the same as the inclusion bodies seen with the light microscope. Naked viral particles were observed in the nucleus of infected cells within or on the edges of the nucleoplasmic aggregates. These particles measured 95-100mμ, in diameter and rarely escaped into the cytoplasm or nuclear vesicles by budding through the nuclear membrane (Fig. 1). The enveloped particles (Fig. 2) formed in this manner measured 150-170mμ in diameter and always had a densely stained nucleoid. The virus in supernatant fluids consisted of naked capsids with 162 hollow, cylindrical capsomeres (Fig. 3). Enveloped particles were not seen in such preparations.

Debates in Dysphagia Management: How Do You Use Evidence-Based Practice in Your Dysphagia Patient Care?

2011 ◽  
Vol 20 (4) ◽  
pp. 121-123
Author(s):  
Jeri A. Logemann
Keyword(s):  
Decision Making ◽  
Patient Care ◽  
Clinical Outcomes ◽  
Clinical Judgment ◽  
Clinical Decision Making ◽  
Evidence Based Practice ◽  
Clinical Decision ◽  
Evidence Based ◽  
Clinical Method ◽  
Do So

Evidence-based practice requires astute clinicians to blend our best clinical judgment with the best available external evidence and the patient's own values and expectations. Sometimes, we value one more than another during clinical decision-making, though it is never wise to do so, and sometimes other factors that we are unaware of produce unanticipated clinical outcomes. Sometimes, we feel very strongly about one clinical method or another, and hopefully that belief is founded in evidence. Some beliefs, however, are not founded in evidence. The sound use of evidence is the best way to navigate the debates within our field of practice.

The Persnickety Pervasiveness of Rating Enhancement in Personality Assessment

2020 ◽  
pp. 1-13
Author(s):  
Alicia A. Stachowski ◽  
John T. Kulas
Keyword(s):  
Response Bias ◽  
Personality Assessment ◽  
Current Paper ◽  
Psychological Measurement ◽  
Shared Sets ◽  
Self Reports ◽  
Original Target ◽  
Target Profile ◽  
Do So ◽  
Normative Influences

Abstract. The current paper explores whether self and observer reports of personality are properly viewed through a contrasting lens (as opposed to a more consonant framework). Specifically, we challenge the assumption that self-reports are more susceptible to certain forms of response bias than are informant reports. We do so by examining whether selves and observers are similarly or differently drawn to socially desirable and/or normative influences in personality assessment. Targets rated their own personalities and recommended another person to also do so along shared sets of items diversely contaminated with socially desirable content. The recommended informant then invited a third individual to additionally make ratings of the original target. Profile correlations, analysis of variances (ANOVAs), and simple patterns of agreement/disagreement consistently converged on a strong normative effect paralleling item desirability, with all three rater types exhibiting a tendency to reject socially undesirable descriptors while also endorsing desirable indicators. These tendencies were, in fact, more prominent for informants than they were for self-raters. In their entirety, our results provide a note of caution regarding the strategy of using non-self informants as a comforting comparative benchmark within psychological measurement applications.

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