11,779 research outputs found
A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry
We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of
the form , where is a toric Fano
manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of
. As applications, we compute the mirror superpotentials for these
manifolds. In particular, this gives a simple proof for the formula of the
mirror superpotential for the Hirzebruch surface .Comment: v3: many minor changes, published in Pacific J. Math.; v2: 16 pages.
Completely rewritten and improve
Does Misclassification of Equity Funds Exist? Evidence from Malaysia
Applying the style analysis developed by Sharpe (1988, 1992), this paper investigates the classification of equity funds in Malaysia. A methodology for creating purified mutual fund style indexes is used to verify existing classifications. The paper concludes that an improper classification of funds would not only cause mismatch between investors objectives and funds’ profile, it also affects the process of income smoothing in the lifecycle of investors. Besides estimating the possible economic impact due to misclassification, this study highlights the importance of a proper classification system of equity funds in Malaysian context and its implication towards investor’s protection.Mutual Fund Classification; Style Analysis; Investor’s Protection
SYZ mirror symmetry for toric Calabi-Yau manifolds
We investigate mirror symmetry for toric Calabi-Yau manifolds from the
perspective of the SYZ conjecture. Starting with a non-toric special Lagrangian
torus fibration on a toric Calabi-Yau manifold , we construct a complex
manifold using T-duality modified by quantum corrections. These
corrections are encoded by Fourier transforms of generating functions of
certain open Gromov-Witten invariants. We conjecture that this complex manifold
, which belongs to the Hori-Iqbal-Vafa mirror family, is inherently
written in canonical flat coordinates. In particular, we obtain an enumerative
meaning for the (inverse) mirror maps, and this gives a geometric reason for
why their Taylor series expansions in terms of the K\"ahler parameters of
have integral coefficients. Applying the results in \cite{Chan10} and
\cite{LLW10}, we compute the open Gromov-Witten invariants in terms of local
BPS invariants and give evidences of our conjecture for several 3-dimensional
examples including K_{\proj^2} and K_{\proj^1\times\proj^1}.Comment: v3: final version, published in JDG 90 (2012), no. 2, 177-250. 71
pages, 14 figures; substantially revised and expande
Crash-Free Sequencing Strategies for Financial Development and Liberalization
This paper uses a stylized model of financial intermediation to characterize the exact circumstances along various paths of economic growth, financial development, and liberalization that can trigger a financial crisis. It shows how to avoid financial crises through proper sequencing of various financial development and liberalization measures. The results of the paper show that naive combinations of financial development and liberalization processes can give rise to financial crises. In some typical situations, in order to avoid a financial crisis, it is important that financial liberalization be accompanied by financial development, in the form of improvements in the financial sectorís efficiencies. In the case of fast growing economies, financial development becomes even more imperative. Copyright 2001, International Monetary Fund
Real Financial Integration among the East Asian Economies: A SURADF Panel Approach
To testify RIP, this study scrutinizes the mean-reversion behavior of bilateral real interest differentials (RIDs) in eight East Asian economies. We incorporate the ASEAN-5, South Korea and China (mainland) with the US and Japan taken as base countries. Four sub-samples within 1976-2004 are being considered to accentuate the effects of institutional changes and financial crises. To rectify the deficiency in extant univariate and panel tests, the newly proposed SURADF statistics by Breuer et al. (2002) is utilized. Overall, the findings are in favor of RIP such that RIDs are found mean-reverting (except China) and with faster adjustment, especially during the post-crisis era. Such outcome is in accord with the enhanced financial integration among the ASEAN-5 and South Korea with their major trading partners, suggesting that further economic cooperation and currency arrangements in the region are bright to preserve potential financial shocks. Conversely, the real financial integration among China-US and China-Japan are not yet empirically recognized notwithstanding the recent surge of capital flows into the mainland.Real Interest Differentials; SURADF Panel Unit Root Test; Half-life; Confidence Intervals; Financial Integration
Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
Let be a compact toric K\"ahler manifold with nef. Let be a regular fiber of the moment map of the Hamiltonian torus action on .
Fukaya-Oh-Ohta-Ono defined open Gromov-Witten (GW) invariants of as virtual
counts of holomorphic discs with Lagrangian boundary condition . We prove a
formula which equates such open GW invariants with closed GW invariants of
certain -bundles over used to construct the Seidel
representations for . We apply this formula and degeneration techniques to
explicitly calculate all these open GW invariants. This yields a formula for
the disc potential of , an enumerative meaning of mirror maps, and a
description of the inverse of the ring isomorphism of Fukaya-Oh-Ohta-Ono.Comment: v4: 44 pages, 3 figures, minor modifications, final version to appear
in DM
Gross fibrations, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds
For a toric Calabi-Yau (CY) orbifold whose underlying toric
variety is semi-projective, we construct and study a non-toric Lagrangian torus
fibration on , which we call the Gross fibration. We apply the
Strominger-Yau-Zaslow (SYZ) recipe to the Gross fibration of to
construct its mirror with the instanton corrections coming from genus 0 open
orbifold Gromov-Witten (GW) invariants, which are virtual counts of holomorphic
orbi-disks in bounded by fibers of the Gross fibration.
We explicitly evaluate all these invariants by first proving an open/closed
equality and then employing the toric mirror theorem for suitable toric
(partial) compactifications of . Our calculations are then applied
to
(1) prove a conjecture of Gross-Siebert on a relation between genus 0 open
orbifold GW invariants and mirror maps of -- this is called the
open mirror theorem, which leads to an enumerative meaning of mirror maps, and
(2) demonstrate how open (orbifold) GW invariants for toric CY orbifolds
change under toric crepant resolutions -- an open analogue of Ruan's crepant
resolution conjecture.Comment: v4: 65 pages, significantly shortened to avoid too much overlap with
arXiv:1006.3830 and arXiv:1206.3994, to appear in JD
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