相关论文: Reducible deformations and smoothing of primitive …
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that the associated reduced curve Y_red is smooth. The subject of this paper is the study of…
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that C=Y_red is smooth. In this case, L=I_C/I_C^2 is a line bundle on C. If Y is of multiplicity 2,…
A primitive multiple curve is a Cohen-Macaulay scheme Y over the field of complex numbers such that the reduced scheme C=Y_red is a smooth curve, and that Y can be locally embedded in a smooth surface. In general such a curve Y cannot be…
A primitive multiple scheme is a complex Cohen-Macaulay scheme $Y$ such that the associated reduced scheme $X=Y_{red}$ is smooth, irreducible, and that $Y$ can be locally embedded in a smooth variety of dimension $\dim(X)+1$. If $n$ is the…
A primitive multiple scheme is a Cohen-Macaulay scheme $Y$ such that the associated reduced scheme $X=Y_{red}$ is smooth, irreducible, and that $Y$ can be locally embedded in a smooth variety of dimension $\dim(X)+1$. If $I_X$ is the ideal…
In this article we show that a wide range of multiple structures on curves arise whenever a family of embeddings degenerates to a morphism $\varphi$ of degree $n$. One could expect to see, when an embedding degenerates to such a morphism,…
A primitive multiple scheme is a Cohen-Macaulay scheme $Y$ such that the associated reduced scheme $X=Y_{red}$ is smooth, irreducible, and that $Y$ can be locally embedded in a smooth variety of dimension $\dim(X)+1$. If $n$ is the…
The primitive curves are the multiple curves that can be locally embedded in smooth surfaces (we will always suppose that the associated reduced curves are smooth). These curves have been defined and studied by C. Banica and O.Forster in…
A multiple (loc. Cohen Macaulay) structure, X, on a space curve C in P3 is said to be primitive if X is locally contained in a smooth surface. We give numerical conditions for C to be a "primitive" set theoretic complete intersection (i.e.…
A simple closed curve in the boundary surface of a handlebody is called primitive if there exists an essential disk in the handlebody whose boundary circle intersects the curve transversely in a single point. The primitive curve complex is…
In this article we present a unified way to smooth certain multiple structures called ropes on smooth varieties. We prove that most ropes of arbitrary multiplicity, supported on smooth curves can be smoothed. By a rope being smoothable we…
We develop a new general method for computing the decomposition type of the normal bundle to a projective rational curve. This method is then used to detect and explain an example of a Hilbert scheme that parametrizes all the rational…
We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform along their Hodge locus in the universal locally trivial…
Let F be a smooth surface in a smooth projective threefold T, and let X=2F be the first infinitesimal neighborhood of X in T. A locally Cohen-Macaulay curve C in X gives rise to two effective divisors on F, namely the curve part P of the…
Some coherent sheaves on projective varieties have a non reduced versal deformation space. For example, this is the case for most unstable rank 2 vector bundles on ${\mathbb P}_2$. In particular, it may happen that some moduli spaces of…
A surface automorphism is strongly irreducible if every essential simple closed curve in the surface has nontrivial geometric intersection with its image. We show that a three-manifold admits only finitely many inequivalent surface bundle…
We constructed a projective moduli space of semistable torsion free sheaves with `fixed determinant' on a reducible curve. When a family of smooth curves degenerates to the reducible curve, our moduli space is a degeneration of the moduli…
We consider finite pencils of Jacobi matrices \[ J_n(w)=A+wB, \] where $A$ is diagonal and $B$ is tridiagonal with zero diagonal. The spectral curve is the affine plane curve \[ \chi_n(\lambda,w)=\det(\lambda I+J_n(w))=0 . \] The main…
A primitive multiple scheme is a Cohen-Macaulay scheme $\bf X$ such that the associated reduced scheme $X={\bf X}_{red}$ is smooth, irreducible, and that $\bf X$ can be locally embedded in a smooth variety of dimension $\dim(X)+1$. If ${\bf…
Let $K$ be a local field of residue characteristic $p$. Let $C$ be a curve over $K$ whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to-$p$ rational torsion…