Related papers: Subvarieties of general type on a general projecti…

We prove analogues of several well-known results concerning rational morphisms between quadrics for the class of so-called quasilinear $p$-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric…

We study smooth projective complex varieties with ample cotangent bundle. Our main result is that in an abelian variety of dimension n, a complete intersection of at least n/2 general hypersurfaces of sufficiently high degrees has ample…

We study various measures of irrationality for hypersurfaces of large degree in projective space and other varieties. These include the least degree of a rational covering of projective space, and the minimal gonality of a covering family…

We investigate geometry of D-affine varieties. Our main result is that a D-affine rational projective surface over an algebraically closed field is a generalised flag variety of a reductive group.

We apply an idea of Levin to obtain a non-truncated second main theorem for non-Archimedean analytic maps approximating algebraic hypersurfaces in subgeneral position. In some cases, for example when all the hypersurfaces are non-linear and…

We study the generalized roundness of finite metric spaces whose distance matrix $D$ has the property that every row of $D$ is a permutation of the first row. The analysis provides a way to characterize subsets of the Hamming cube $\{ 0, 1…

We describe a multivariable polynomial invariant for certain class of non isolated hypersurface singularities generalizing the characteristic polynomial on monodromy. The starting point is an extension of a theorem due to Le Dung Trang and…

We consider hypersurfaces of finite type in a direct product space ${\mathbb R}^2 \times {\mathbb R}^2$, which are analogues to real hypersurfaces of finite type in ${\mathbb C}^2$. We shall consider separately the cases where such…

Consider a component of the Hilbert scheme whose general point corresponds to a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such a component when X is P^3,…

In this paper we construct, for every n, smooth varieties of general type of dimension n with the first $\lfloor \frac{n-2}{3} \rfloor$ plurigenera equal to zero. Hacon-McKernan, Takayama and Tsuji have recently shown that there are numbers…

We prove that the complement of a very general pair of hypersurfaces of total degree $2n$ in $\mathbb{P}^n$ is algebraically hyperbolic modulo a proper closed subvariety. This provides evidence towards conjectures of Lang-Vojta and…

We consider surjective endomorphisms f of degree > 1 on projective manifolds X of Picard number one and their f^{-1}-stable hypersurfaces V, and show that V is rationally chain connected. Also given is an optimal upper bound for the number…

We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections…

In this paper, we compute the contributions from double cover maps to genus 0 degree 2 Gromov-Witten invariants of general type projective hypersurfaces. Our results correspond to a generalization of Aspinwall-Morrison formula to general…

We associate to any irreducible germ S of complex quasi-ordinary hypersurface an analytically invariant semigroup. We deduce a direct proof (without passing through their embedded topological invariance) of the analytical invariance of the…

We show that any hyperplane section of a variety which is the inverse image of a smooth variety of dimension at least 2 by an endomorphism (wich is not an automorphism) of the projective space, is linearly complete. We stress the case of…

In many cases (e.g. for many Segre or Segre embeddings of multiprojective spaces) we prove that a hypersurface of the $b$-secant variety of $X\subset \mathbb {P}^r$ has $X$-rank $>b$. We prove it proving that the $X$-rank of a general point…

Let $n=2,3,4,5$ and let $X$ be a smooth complex projective hypersurface of $\mathbb P^{n+1}$. In this paper we find an effective lower bound for the degree of $X$, such that every holomorphic entire curve in $X$ must satisfy an algebraic…

We introduce a mock toric variety, a generalization of a toric variety. For a non-toric example, Del-Pezzo surfaces are mock toric varieties. These new varieties inherit some properties of mock toric varieties. In application, we give…

Linearly projecting smooth projective varieties provides a method of obtaining hypersurfaces birational to the original varieties. We show that in low dimension, the resulting hypersurfaces only have Du Bois singularities. Moreover, we…