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Viada Evelina

Publications and source records attributed to Viada Evelina.

5 recordsLinked to original sources
arXiv2009

A functorial lower bound for the essential minimum of varities in a power of an elliptic curve

A subvariety V of an abelian variety is `translate' if it is the union of translates of proper algebraic subgroups. An irreducible V is `transverse' if it is not contained in any translate variety. Effective sharp lower bounds for a transverse subvarieties of a power of an elliptic curve E are known. Here, we prove a sharp lower bound for the essential minimum of non-translate subvarieties of such a power E^g.

math.NT↗
arXiv2009

Non-dense sets of subvarieties in a power of an elliptic curve

Let V be an algebraic variety embedded in a power of an elliptic curve, both defined over the algebraic numbers. We show that the set of algebraic points of V which are of bounded height and which satisfy certain algebraic conditions are a non-dense subset of V. This result has implications in the context of the Pink-Zilber Conjecture and Mordel-Lang plus Bogomolov Theorem.

math.NT↗
arXiv2008

The optimality of the Boundedness Height Conjecture

We show that the Boundedness Height Conjecture is optimal; all varieties in a power of an elliptic curve which do not satisfy the hypothesis neither satisfy the thesis. The Bounded Height Conjecture is known to hold for varieties in a power of an elliptic curve. We also present some examples and remarks.

math.NT↗
arXiv2008

Lower bounds for the normalized height and non-dense subsets of varieties in an abelian variety

This work is the third part of a series of papers. In the first two we consider curves and varieties in a power of an elliptic curve. Here we deal with subvarieties of an abelian variety in general. Let V be an irreducible variety of dimension d embedded in an abelian variety A, both defined over the algebraic numbers. We say that V is weak-transverse if V is not contained in any proper algebraic subgroup of A, and transverse if it is not contained in any translate of such a subgroup. Assume a conjectural lower bound for the normalized height of V. For V transverse, we prove that the algebraic points of bounded height of V which lie in the union of all algebraic subgroups of A of codimension at least d+1 translated by the points close to a subgroup G of finite rank are non Zariski-dense in V. If G has rank zero, it is sufficient to assume that V is weak-transverse. The notion of closeness is defined using a height function.

math.NT↗