Related papers: Sur le morphisme de Barth

In this article we generalize the injectivity of the push-forward homomorphism at the level of Chow groups, induced by the closed embedding of $\Sym^m C$ into $\Sym^n C$ for $m\leq n$, where $C$ is a smooth projective curve, to symmetric…

Vector bundles and double vector bundles, or $2$-fold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids. It is known that all these…

We calculate the Chern classes and Chern numbers for the natural almost Hermitian structures of the partial flag manifolds F_n=SU(n+2)/S(U(n)\times U(1)\times U(1)). For all n>1 there are two invariant complex algebraic structures, which…

We construct master spaces for oriented torsion free sheaves coupled with morphisms into a fixed reference sheaf. These spaces are projective varieties endowed with a natural $\C^*$-action. The fixed point set of this action contains the…

We show that any pointed, preordered module map $\mathfrak{BF}_{\mathrm{gr}}(E) \to \mathfrak{BF}_{\mathrm{gr}}(F)$ between Bowen-Franks modules of finite graphs can be lifted to a unital, graded, diagonal preserving $\ast$-homomorphism…

In this paper we consider the algebra of upper triangular matrices UT$_n(F)$, endowed with a $\mathbb{Z}_2$-grading (superalgebra) and equipped with a superinvolution. These structures naturally arise in the context of Lie and Jordan…

Let k be an algebraically closed field of characteristic 0, and let $A = k[x,y]/(f)$ be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e. a graded…

We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism…

We show the Frobenius pullback of a general semi-stable vector bundle in the moduli space of vector bundles with fixed rank and degree is still semi-stable by deformation trick. We then present several applications of the main theorem.

We decompose each moduli space of semistable sheaves on the complex projective plane with support of dimension one and degree four into locally closed subvarieties, each subvariety being the good or geometric quotient of a set of morphisms…

Moduli spaces of semistable torsion-free sheaves on a K3 surface $X$ are often holomorphic symplectic varieties, deformation equivalent to a Hilbert scheme parametrizing zero-dimensional subschemes of $X$. In fact this should hold whenever…

We describe new irreducible components of the moduli space of rank $2$ semistable torsion free sheaves on the three-dimensional projective space whose generic point corresponds to non-locally free sheaves whose singular locus is either…

Let $f$ be a birational map of ${\bf C}^d$, and consider the degree complexity, or asymptotic degree growth rate $\delta(f)=\lim_{n\to\infty}({\rm deg}(f^n))^{1/n}$. We introduce a family of elementary maps, which have the form $f=L\circ…

In this paper, we establish general stratawise higher jet evaluation transversality of $J$-holomorphic curves for a generic choice of almost complex structures $J$ tame to a given symplectic manifold $(M,\omega)$. Using this transversality…

In this paper we begin to study curves on a weighted projective plane with one trivial weight, ${\mathbb P}(1,m,n)$, by determining the genus of curves of Fermat type. These are curves defined by a ``homogeneous'' polynomial analagous to…

This is the revised version of our previous preprint. In this paper, we establish a generic smoothness result for moduli space of semistable sheaves of arbitrary rank over surfaces provided that the second Chern class of the sheaves is…

Let $M(n,\xi)$ be the moduli space of stable vector bundles of rank $n\geq 3$ and fixed determinant $\xi$ over a smooth projective algebraic curve $X$ over $\mathbb{C}$ of genus $g\geq 4.$ We use the gonality of the curve and $r$-Hecke…

Let $k$ be a field, let ${\sf C}$ be a $k$-linear abelian category, let $\underline{\mathcal{L}}:=\{\mathcal{L}_{i}\}_{i \in \mathbb{Z}}$ be a sequence of objects in ${\sf C}$, and let $B_{\underline{\mathcal{L}}}$ be the associated orbit…

It goes back to Ahlfors that a real algebraic curve admits a real-fibered morphism to the projective line if and only if the real part of the curve disconnects its complex part. Inspired by this result, we are interested in characterising…

Let X be a geometrically smooth n-dimensional projective algebraic complex hypersurface in P^{n+1}(C). Using Green-Griffiths jets, we establish the existence of nonzero global algebraic differential equations that must be satisfied by every…