相关论文: The Abel-Jacobi map of the space of conics for dou…

In this paper, we consider the moduli space $\cSU_C(r,\cO_C)$ of rank $r$ semistable vector bundles with trivial determinant on a smooth projective curve $C$ of genus $g$. When the rank $r=2$, F. Kirwan constructed a smooth log resolution…

We solve the problem of inversion of an extended Abel-Jacobi map $$ \int_{P_{0}}^{P_{1}}\omega +...+\int_{P_{0}}^{P_{g+n-1}}\omega ={\bf z}, \qquad \int_{P_{0}}^{P_{1}}\Omega_{j1}+... +\int_{P_{0}}^{P_{g+n-1}}\Omega_{j1} =Z_{j},\quad…

Let \(X\subset \mathbb{P}^{n+1}\) be a smooth cubic hypersurface, and let \(F(X)\) be the variety of lines on \(X\). We prove the surjectivity of the cylinder maps on the Chow groups of \(F(X)\) and \(X\) if \(X\) contains a one-cycle of…

The purpose of this article is to study the deformations of smooth surfaces $X$ of general type whose canonical map is a finite, degree 2 morphism onto a minimal rational surface or onto $\mathbf F_1$, embedded in projective space by a very…

We develop an equivariant version of the formalism of intermediate Jacobian torsor obstructions, and apply it to conic bundles over rational surfaces, quadric surface bundles over $\mathbb P^1$, and Fano threefolds.

General hyperplane sections of a Fano threefold $Y$ of index 2 and Picard rank 1 are del Pezzo surfaces, and their Picard group is related to a root system. To the corresponding roots, we associate objects in the Kuznetsov component of $Y$…

We study, as hypersurfaces in toric varieties, elliptic Calabi-Yau fourfolds for F-theory compactifications dual to E8xE8 heterotic strings compactified to four dimensions on elliptic Calabi-Yau threefolds with some choice of vector bundle.…

We consider an integrable system in five unknowns having three quartics invariants. We show that the complex affine variety defined by putting these invariants equal to generic constants, completes into an abelian surface; the jacobian of a…

We construct a three-parameter family of non-hyperelliptic and bielliptic plane genus-three curves whose associated Prym variety is two-isogenous to the Jacobian variety of a general hyperelliptic genus-two curve. Our construction is based…

In this paper we study the cohomology of smooth projective complex surfaces $S$ of general type with invariants $p_g = q = 2$ and surjective Albanese morphism. We show that on a Hodge-theoretic level, the cohomology is described by the…

A generalized Kummer surface $X$ obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 contains a $9\mathbf{A}_{2}$-configuration of $(-2)$-curves. Such a configuration plays the role of the…

Let $X$ be a surface of general type with maximal Albanese dimension: if $K_X^2<\frac{9}{2}\chi(\mathcal{O}_X)$, one has $K_X^2\geq 4\chi(\mathcal{O}_X)+4(q-2)$. We give a complete classification of surfaces for which equality holds for…

We discuss the space of sections and certain bisections on a quadric surfaces bundle $X$ over a smooth curve. The Abel-Jacobi from these spaces to the intermediate Jacobian will be shown to be dominant with rationally connected fibers. As…

In [CS01, Page 109] Grothendieck sketches the construction of a complex J_*(X) or commutative pro-algebraic groups, associated to a smooth variety X, and for which each J_i(X) is a product of local factors called the local generalized…

We define a period map for classical Campedelli surfaces, using a covering trick as in the case of Enriques surfaces: the period map is shown to come from a family of Enriques surfaces, obtained as quotients of the Campedelli surface by an…

In this paper we give local conditions to the existence of Abel maps for nodal curves that are limits of Abel maps for smooth curves. We use this result to construct Abel maps for any degree for nodal curves with two components.

Let $(X ,x_0)$ be a pointed smooth proper variety defined over an algebraically closed field. The Albanese morphism for $(X ,x_0)$ produces a homomorphism from the abelianization of the $F$-divided fundamental group scheme of $X$ to the…

We propose an algebraic method for the classification of branched Galois covers of a curve $X$ focused on studying Galois ring extensions of its geometric adele ring $\A_{X}$. As an application, we deal with cyclic covers; namely, we…

We study the moduli space of framed quadratic differentials with prescribed singularities parameterized by a decorated marked surface with punctures (DMSp), where simple zeros, double poles and higher order poles respectively correspond to…

We study the geometry and arithmetic of the curves $C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces $P$. We prove a Torelli theorem in this context and give a geometric proof of the fact that $P$ has quaternionic…