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Gepner-Type Stability Condition

A Gepner-type stability condition is a Bridgeland stability condition for which a specified autoequivalence rotates the central charge and translates the semistable phases by a fixed amount. For a smooth complex quintic threefold X subset P^4, put Phi=T_(O_X) degrees(- tensor O_X(1)), using the spherical twist. Toda's normalized quintic formulation requires

Z(PhiE)=e^(2pii/5)Z(E),
(1)
Phi(P(phi))=P(phi+2/5),
(2)
Z(O_x)=-1
(3)

for every closed point x.

See also

Bridgeland Stability Condition, Derived Category, Grothendieck Group, Hypersurface, Spherical Twist

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References

Toda, Y. "Gepner Point and Strong Bogomolov-Gieseker Inequality for Quintic 3-Folds." In Higher Dimensional Algebraic Geometry: In Honour of Professor Yujiro Kawamata's Sixtieth Birthday (Ed. K. Oguiso, C. Birkar, S. Ishii, and S. Takayama). Tokyo, Japan: Mathematical Society of Japan, pp. 381-405, 2017. https://doi.org/10.2969/aspm/07410381.

Cite this as:

Weisstein, Eric W. "Gepner-Type Stability Condition." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Gepner-TypeStabilityCondition.html

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