Do you want to publish a course? Click here

The exceptional locus in the Bertini irreducibility theorem for a morphism

103   0   0.0 ( 0 )
 Added by Bjorn Poonen
 Publication date 2020
  fields
and research's language is English




Ask ChatGPT about the research

We introduce a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing over a finite field. Extending a result of Benoist, we prove that for a morphism $phi colon X to mathbb{P}^n$ such that $X$ is geometrically irreducible and the nonempty fibers of $phi$ all have the same dimension, the locus of hyperplanes $H$ such that $phi^{-1} H$ is not geometrically irreducible has dimension at most $operatorname{codim} phi(X)+1$. We give an application to monodromy groups above hyperplane sections.



rate research

Read More

86 - Xiaozong Wang 2020
Let $mathcal{X}$ be a regular projective arithmetic variety equipped with an ample hermitian line bundle $overline{mathcal{L}}$. We prove that the proportion of global sections $sigma$ with $leftlVert sigma rightrVert_{infty}<1$ of $overline{mathcal{L}}^{otimes d}$ whose divisor does not have a singular point on the fiber $mathcal{X}_p$ over any prime $p<e^{varepsilon d}$ tends to $zeta_{mathcal{X}}(1+dim mathcal{X})^{-1}$ as $drightarrow infty$.
The goal of this article is to prove the comparison theorem between algebraic and topological nearby cycles of a morphism without slopes. We prove in particular that for a family of holomorphic functions without slopes, if we iterate comparison isomorphisms for nearby cycles of each function the result is independent of the order of iteration.
161 - Ulrich Goertz , Chia-Fu Yu 2009
We study moduli spaces of abelian varieties in positive characteristic, more specifically the moduli space of principally polarized abelian varieties on the one hand, and the analogous space with Iwahori type level structure, on the other hand. We investigate the Ekedahl-Oort stratification on the former, the Kottwitz-Rapoport stratification on the latter, and their relationship. In this way, we obtain structural results about the supersingular locus in the case of Iwahori level structure, for instance a formula for its dimension in case $g$ is even.
Let $k$ be a field finitely generated over the finite field $mathbb F_p$ of odd characteristic $p$. For any K3 surface $X$ over $k$ we prove that the prime to $p$ component of the cokernel of the natural map $Br(k)to Br(X)$ is finite.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا