Gepner symmetry and large-volume stability on threefolds

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Proves Toda’s Gepner conjecture for every smooth complex quintic threefold, constructing a numerical Bridgeland stability condition with the prescribed phase shift 2/5. Also constructs numerical Bridgeland stability conditions at every sufficiently large volume on all smooth projective complex threefolds with trivial canonical bundle, with the exact ordinary and square-root-Todd central charges.

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The paper states

Theorem 1.1

In A Gepner stability condition on every smooth quintic threefold

Possible match to OpenAI’s description, selected from the papers’ main statements because it shares the most wording. No review confirming the selection is recorded.

Three other possible matches are listed below the card, among them Theorem 1.1 (Exact large-volume charges on a real sector) in Prescribed large-volume charges on threefolds with trivial canonical bundle and Theorem 1.2 (Uniform strong inequality) in Prescribed large-volume charges on threefolds with trivial canonical bundle.

Every smooth complex quintic threefold admits a numerical Bridgeland stability condition \sigma=(Z,\mathcal P) with the support property on \Knum(X)_{\R} such that, for every E\in\D and \varphi\in\R,

Z(\Phi E)=e^{2\pi i/5}Z(E),\qquad \Phi\bigl(\mathcal P(\varphi)\bigr)=\mathcal P(\varphi+2/5),\qquad Z(\OO_x)=-1

for every closed point x\in X.

Three more possible matches

Theorem 1.1 (Exact large-volume charges on a real sector) in Prescribed large-volume charges on threefolds with trivial canonical bundle.
Theorem 1.2 (Uniform strong inequality) in Prescribed large-volume charges on threefolds with trivial canonical bundle.
Corollary 1.3 (A parabolic region with trivial correction) in Prescribed large-volume charges on threefolds with trivial canonical bundle.

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A Gepner stability condition on every smooth quintic threefold

Undated, current edition.

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We prove Toda’s normalized quintic Gepner conjecture. On every smooth complex quintic threefold, we construct a numerical Bridgeland stability condition for which tensoring by the hyperplane bundle, followed by the spherical twist at the structure sheaf, increases phase by 2/5.

Prescribed large-volume charges on threefolds with trivial canonical bundle

Undated, current edition.

Read it here PDF

Let X be a smooth projective complex threefold with trivial canonical bundle. We construct numerical Bridgeland stability conditions with the exact ordinary and square-root-Todd central charges at every sufficiently large volume. One volume threshold works on an open set of real twists and ample directions. The resulting stability conditions have the support property on the full numerical Grothendieck group and stable point sheaves. Separately, on every smooth projective complex threefold we prove a strong tilt inequality above a volume threshold uniform in the object and twist along a fixed polarization.

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