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Sheng-Yong Pan

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Preprint Aug 2026

Recollements of derived categories from $n$-term big tilting complexes

Let $A$ be a ring, let ${\bf T}$ be a finite-term big tilting complex over $A$, and choose a bounded projective representative $\cpx{P}$ of ${\bf T}$. Put $B=\End_{\D{A}}(\cpx{P})$. We prove that the kernel of the associated derived tensor functor ${\bf R}:\D{B}\to\D{A}$ is equivalent, through the derived inclusion, to...

Sheng-Yong Pan, Huabo Xu · 1 citation

Preprint Oct 2026

The $E_6$ normal forms: semisimple deformations, geometry, DT invariants, and the $E_{6,\infty}$ order

We study the completed Jacobi algebras of $x^3+xy^3+p(y)$ for $\operatorname{ord}_yp=n\ge4$. The explicit normal-form morsification, the filtered length and centre proofs, and the cyclic terminal identities give finite free semisimple deformations. For every parameter of finite order we construct a polynomial curve nei...

Sheng-Yong Pan · 0 citations

Preprint Oct 2026

Counterexamples to the Polishchuk--Van den Bergh conjecture on curves

We construct effective finite group actions on smooth projective complex curves for which Conjecture A of Polishchuk and Van den Bergh fails. For every $h\geq1$, an explicit $S_3$ action on the smooth projective model of $y^2=t^{12h-5}+t$ has quotient of genus $h$ and exactly one ramification orbit, with inertia of ord...

Sheng-Yong Pan · 0 citations