Related papers: Normal forms for ordinary differential operators, …

We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of the topological and algebraic…

This article aims to extend classical homological results about the rational normal curves to analogues in weighted projective spaces. Results include determinantality and nonstandard versions of quadratic generation and the Koszul…

This article gives a characterization of quotients of complex tori by finite groups acting freely in codimension two in terms of a numerical vanishing condition on the first and second Chern class. This generalizes results previously…

In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can be studied using the technique of matrix…

We propose a sheaf-theoretic approach to the theory of differential calculi on quantum principal bundles over non-affine bases. After recalling the affine case we define differential calculi on sheaves of comodule algebras as sheaves of…

This article treats compactifications of the space of generalized spin curves. Generalized spin curves, or $r$-spin curves, are pairs $(X,L)$ with $X$ a smooth curve and $L$ a line bundle whose r-th tensor power is isomorphic to the…

In this paper, we describe an algorithm that, for a smooth connected curve $X$ over a field $k$ with normal completion having arithmetic genus $p_a(X)$, a finite locally constant sheaf $\mathcal A$ on $X_{et}$ of abelian groups of torsion…

We study the first "derived functors of unramified cohomology" in the sense of arXiv:1506.08385 [math.AG], applied to the sheaves $\mathbf{G}_m$ and $\mathcal{K}_2$. We find interesting connections with classical cycle-theoretic invariants…

Let $X/S$ be a smooth family of smooth projective varieties, where $S$ is a smooth affine curve over a field $k$ of characteristic $0.$ We relate the differential fundamental groupoid scheme of $X/k$ with the differential fundamental…

Special kinds of rank 2 vector bundles with (possibly irregular) connections on P^1 are considered. We construct an equivalence between the derived category of quasi-coherent sheaves on the moduli stack of such bundles and the derived…

We prove formulas for the cohomology and the extension groups of tautological bundles on punctual Quot schemes over complex smooth projective curves. As a corollary, we show that the tautological bundle determines the isomorphism class of…

Consider a hyperelliptic curve of genus $2$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $6$ Weierstrass points. We classify the structure of the potentially stable reduction of such…

We study locally free sheaves of rank two on the projective line over the integers, especially indecomposable ones. Subsequently we apply various concepts of Arakelov geometry to these sheaves. We compute for example the arithmetic Chern…

Suppose $X$ is a hyperelliptic curve of genus $g$ defined over an algebraically closed field $k$ of characteristic $p=2$. We prove that the de Rham cohomology of $X$ decomposes into pieces indexed by the branch points of the hyperelliptic…

We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for…

Let $F$ be a torsionfree semistable coherent sheaf on a polarized normal projective variety. We prove that $F$ has a unique maximal locally free subsheaf $V$ such that $F/V$ is torsionfree and $V$ admits a filtration of subbundles for which…

Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as the quintic 3-fold. By two different wall-crossing arguments we prove two different explicit formulae relating rank 0 Donaldson-Thomas…

Working over imperfect fields, we give a comprehensive classification of genus-one curves that are regular but not geometrically regular, extending the known case of geometrically reduced curves. The description is given intrinsically, in…

We analyse infinitesimal deformations of morphisms of locally free sheaves on a smooth projective variety $X$ over an algebraically closed field of characteristic zero. In particular, we describe a differential graded Lie algebra…

We introduce an exact category of torsion-free constructible tori and an abelian category of constructible tori over a Dedekind scheme with perfect residue fields. The first one has an explicit description as $2$-term complexes of smooth…