Bertini type results and their applications

TL;DR

This paper proves Bertini type theorems and explores their applications in algebraic geometry, including Lefschetz theorems for Nori fundamental groups and properties of lisse -adic sheaves on smooth quasi-projective varieties.

Contribution

It introduces new Bertini type results and demonstrates their utility in fundamental group theory and sheaf theory for algebraic varieties.

Findings

Bertini type theorems are established for normal varieties.

Applications include Lefschetz theorems for Nori fundamental groups.

Certain smooth quasi-projective varieties contain curves preserving sheaf irreducibility.

Abstract

We prove Bertini type theorems and give some applications of them. The applications are in the context of Lefschetz theorem for Nori fundamental group for normal varieties as well as for geometric formal orbifolds. In another application, it is shown that certain class of a smooth quasi-projective variety contains a smooth curve such that irreducible lisse \ell-adic sheaves on the variety with "ramification bounded by a branch data" remains irreducible when restricted to the curve.