Log Abelian Varieties over a Log Point

A Structure Theorem for Strongly Abelian Varieties with Few Models

Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography

We call a simple abelian variety over Fp super-isolated if its (Fp-rational) isogeny class contains no other varieties. The motivation for considering these varieties comes from concerns about isogeny based attacks on the discrete log problem. We heuristically estimate that the number of super-isolated elliptic curves over Fp with prime order and p ≤ N , is roughly Θ̃( √ N). In contrast, we prov...

Toroidal Crossings and Logarithmic Structures

We generalize Friedman’s notion of d-semistability, which is a necessary condition for spaces with normal crossings to admit smoothings with regular total space. Our generalization deals with spaces that locally look like the boundary divisor in Gorenstein toroidal embeddings. In this situation, we replace d-semistability by the existence of global log structures for a given gerbe of local log ...

Introduction to the Theory of Quasi-log Varieties

This paper is a gentle introduction to the theory of quasi-log varieties by Ambro. We explain the fundamental theorems for the log minimal model program for log canonical pairs. More precisely, we give a proof of the base point free theorem for log canonical pairs in the framework of the theory of quasi-log varieties.

Some fixed point theorems and common fixed point theorem in log-convex structure

Some fixed point theorems and common fixed point theorem in Logarithmic convex structure areproved.