Pieter Belmans
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Fortnightly links (104)

Apr 13, 2020 • Pieter Belmans

posted in:
  • mathematics
tags:
  • fortnightly links
  • Alexander Perry: The integral Hodge conjecture for two-dimensional Calabi-Yau categories is a must-read (if you have the time and necessary background).

  • Indranil Biswas, Tomas L. Gomez: On vector bundles over moduli spaces trivial on Hecke curves proves an interesting result for moduli of vector bundles on a curve, whose geometry I find very interesting. It's analogous to the result that if $\mathcal{E}$ is a vector bundle on $\mathbb{P}^n$, such that $\mathcal{E}|_L\cong\mathcal{O}_{\mathbb{P}^1}^{\oplus r}$ for every line on $\mathbb{P}^n$, then $\mathcal{E}$ is itself trivial. For $\mathrm{M}_C(r,\mathcal{L})$, the same result holds, where the role of lines is played by "rational curves of minimal degree", also known as Hecke curves (which have an explicit modular interpretation).

  • David Favero, Daniel Kaplan, Tyler L. Kelly: A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles gives a counterexample to the Lekili-Ueda conjecture on the existence of a full exceptional collection of line bundles for a Landau–Ginzburg model, which is itself analogous to King's conjecture on the existence of a full exceptional collection of line bundles for a smooth projective toric variety. The latter is known to be false since 2006, by Hille–Perling. Now the Landau--Ginzburg model version for invertible polynomials is also known to be false.

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