On stability conditions for the quintic threefold

We study the Clifford type inequality for a particular type of curves $C_{2,2,5}$, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macr\`i, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in $\mathbf{P}^4_{\mathbb C}$.Comment: pre-journal version, 32 pages, 7 figures, comments are very welcome

Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces

Let X be a projective smooth holomorphic Poisson surface, in other words, whose anti-canonical divisor is effective. We show that moduli spaces of certain Bridgeland stable objects on X are smooth. Moreover, we construct Poisson structures on these moduli spaces.Comment: We would like to thank Sergey Mozgovoy for pointing out a mistake in the first and journal version of this paper. Our result only holds for $H$ that is numerically parallel to $K_X

Brill-Noether theory for curves on generic Abelian surfaces

We completely describe the Brill–Noether theory for curves in the primitive linear system on generic abelian surfaces, in the following sense: given integers d and r, consider the variety Vrd(|H|) parametrizing curves C in the primitive linear system (|H|) together with a torsion-free sheaf on C of degree d and r+1 global sections. We give a necessary and sufficient condition for this variety to be non-empty, and show that it is either a disjoint union of Grassmannians, or irreducible. Moreover, we show that, when non-empty, it is of expected dimension

Fully faithful functors, skyscraper sheaves, and birational equivalence

Let $X$ and $Y$ be two smooth projective varieties such that there is a fully faithful exact functor from $D^b(\mathrm{Coh}(X))$ to $D^b(\mathrm{Coh}(Y))$. We show that $X$ and $Y$ are birational equivalent if the functor maps one skyscraper sheaf to a skyscraper sheaf. Further assuming that $X$ and $Y$ are of the same dimension, we show that if $X$ has ample canonical bundle and $H^0(X ,K_X)\neq 0$, or if $X$ is a K3 surface with Picard number one, then $Y$ is birational to a Fourier--Mukai partner of $X$.Comment: 20 pages. Comments are very welcome

Incentive Mechanism Design Aiming at Deflated Performance Manipulation in Retail Firms: Based on the Ratchet Effect and the Reputation Effect

Store managers in retail firms are often offered a performance-based compensation scheme accompanied with a performance target by the headquarters. The headquarters adjusts the performance target based on store managers’ historical performance and therefore generates the ratchet effect. Consequently, store managers may downward manipulate performance, that is, deflated performance manipulation, so as to weasel out of target growth and smooth performance growth. However, the reputation effect that seeks fame by store managers can restrain deflated performance manipulation. We model a dynamic agency setting in which both the ratchet effect and the reputation effect are related to the store manager’s compensation scheme, and the store manager has to balance her effort and deflated performance manipulation. Our findings reveal that the ratchet effect and environmental volatility jointly determine the existence of deflated performance manipulation, yet the reputation effect can restrain it with increasing environmental volatility. In addition, deflated performance manipulation is inevitable when environmental volatility is large enough, and explicit incentives may promote deflated performance manipulation