Related papers: Smooth hypersurfaces in abelian varieties over ari…

We study a natural generalization of transversally intersecting smooth hypersurfaces in a complex manifold: hypersurfaces, whose components intersect in a transversal way but may be themselves singular. Such hypersurfaces will be called…

In this work we show two results about approximating, with respect to the compact-open topology, mapping classes on surfaces of infinite-type by quasi-conformal maps, in particular we are interested in density results. The first result is…

We prove a Lefschetz hypersurface theorem for abelian fundamental groups allowing wild ramification along some divisor. In fact, we show that isomorphism holds if the degree of the hypersurface is large relative to the ramification along…

Let $Y$ be a smooth quasi-projective complex variety equipped with a simple normal crossings compactification. We show that integral points are potentially dense in the (relative) character varieties parametrizing $SL_2$-local systems on…

Let $X$ be any smooth simply connected projective surface. We consider some moduli space of pure sheaves of dimension one on $X$, i.e. $\mhu$ with $u=(0,L,\chi(u)=0)$ and $L$ an effective line bundle on $X$, together with a series of…

Let $X$ be a smooth projective hypersurface defined over $\mathbb{Q}$. We provide new bounds for rational points of bounded height on $X$. In particular, we show that if $X$ is a smooth projective hypersurface in $\mathbb{P}^n$ with $n\geq…

The endomorphism ring End(A) of an abelian variety A is an order in a semi-simple algebra over Q. The co-index of End(A) is the index to a maximal order containing it. We show that for abelian varieties of fixed dimension over any…

Given a minimal surface equipped with a generically finite map to an Abelian variety, we give an optimal bound on the canonical degree of a rational or an elliptic curve. As a corollary, we obtain the finiteness of rational and elliptic…

The moduli space of principally polarized abelian varieties with real structure and with level $N=4m$ structure (with $m \ge 1$) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over $\mathbb…

We prove that every smooth affine variety of dimension $d$ embeds into every simple algebraic group of dimension at least $2d+2$. We do this by establishing the existence of embeddings of smooth affine varieties into the total space of…

Let $X$ be a smooth projective variety defined over a finite field. We show that any algebraic $1$-cycle on $X$ is rationally equivalent to a smooth $1$-cycle, which is a $\mathbb{Z}$-linear combination of smooth curves on $X$. We also…

The existence of a smooth complete strictly locally convex hypersurface with prescribed scalar curvature and asymptotic boundary at infinity in $\mathbb{H}^{3}$ is proved under the assumption that there exists a strictly locally convex…

Under a hypothesis on $k$, $d$ and $n$ that is almost the best possible, we prove that for every smooth degree $d$ hypersurface in $P^n$, the $k$-plane sections dominate the moduli space of degree $d$ hypersurface in $P^k$. Using this we…

In this paper we obtain an explicit formula for the number of hypersurfaces in a compact complex manifold X (passing through the right number of points), that has a simple node, a cusp or a tacnode. The hypersurfaces belong to a linear…

Let $A$ be an abelian variety over the function field $K$ of a curve over a finite field. We describe several mild geometric conditions ensuring that the group $A(K^{\rm perf})$ is finitely generated and that the $p$-primary torsion…

In this paper we discuss the notion of smoothness in complex algebraic supergeometry and we prove that all affine complex algebraic supergroups are smooth. We then prove the stabilizer theorem in the algebraic context, providing some useful…

We construct smooth rational real algebraic varieties of every dimension $\ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.

One of the simplest examples of a smooth, non degenerate surface in P^4 is the quintic elliptic scroll. It can be constructed from an elliptic normal curve E by joining every point on E with the translation of this point by a non-zero…

Let $R$ be a complete discrete valuation ring with fraction field of characteristic $0$ and algebraically closed residue field of characteristic $p>0$. Let $X_R \to \mathrm{Spec}(R)$ be a smooth projective morphism of relative dimension…

We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We shall concern only the quotient singularity of hypersurface type. The abelian group $A_r(n)$ for $A$-type…