Aug 2026· 6 citations· ⚡ 2 influential· 28 references
Mathematics
Abstract
We establish Chudnovsky's Conjecture and, more generally, Demailly's Conjecture for any finite set of points in $\mathbb{P}^n_k$, where $k$ is an algebraically closed field of characteristic 0. The key idea of passing to positive characteristic, as well as the broad plan of the proof, was suggested by ChatGPT-5.6 Sol. All mathematical arguments and proofs in this paper were developed, written, and verified by the authors.
We completely characterize when a general curve of genus $g$ admits a non-degenerate degree $d$ map to projective space $\mathbb{P}^r$, that is $k$-secant along a linear space $\mathbb{P}^s \subset \mathbb{P}^r$ and deforms in a smooth family of expected dimension. This gives an optimal improvement of a theorem of Fark...
We prove a closed formula for DT4 invariants of one dimensional stable sheaves on the total space of $\mathcal{O}_{\mathbb{P}^2}(-1,-2)$ for all degree curve classes. During the proof, orientations of moduli spaces are chosen in a canonical way. Combining with Gopakumar-Vafa type invariants proposed and computed by Kle...
Abstract We prove a conjecture of Manin and Orlov: the moduli space script upper M overbar Subscript 0 comma n M¯0,n
$\overline{\mathcal{M}}_{0,n}$
of stable rational curves with n marked points admits a full exceptional collection that is equivariant under the action of the symmetric group upper S Subscript n Sn
$S_n...
Ana-Maria Castravet, J. Tevelev· Compositio Mathematica· 0 citations
The principal matroid determinant $E_L$ of a linear space $L \subseteq \mathbb{P}^n$ has been introduced in recent work by Matsubara-Heo and Telen. In this paper, we give the complete factorization of this polynomial into its irreducible components, proving a conjecture of the aforementioned authors. Our methods rely o...
Clara Briand, Leonie Kayser, Julian Weigert· 1 citation
For an algebraically closed field $k$ of characteristic $p>0$, we study unramified $\mathbf{Z}_p$-towers $\{X_n\}_{n\ge 0}$ of smooth, projective and connected curves over $k$. Our main result provides an Iwasawa-theoretic description of the Newton polygons of their Jacobians, establishing that the slopes of the new pa...
We recast the Lange-Stuhler theorem as the universal property of a $2$-cartesian square of classifying stacks. This formulation shows that every Frobenius-periodic vector bundle of rank $r$ on an arbitrary fibered category in characteristic $p>0$ is trivialized by a finite \'etale torsor, without geometric hypotheses o...
Lei Zhang· 0 citations
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