arXiv subjects

Nikolaos Tziolas

Publications and source records attributed to Nikolaos Tziolas.

20 records · Page 2Linked to original sources

arXiv2001

Infinitesimal Extensions of P^1 and their Hilbert Schemes

In order to calculate the multiplicity of an isolated rational curve C in a local complete intersection variety X, i.e. the length of the Hilbert scheme of X at [C], it is important to study infinitesimal neighborhoods of the curve in X. This is equivalent to infinitesimal extensions of P^1 by locally free sheaves. In this paper we study infinitesimal extensions of P^1, determine their structure and obtain upper and lower bounds for the length of the local rings of their Hilbert schemes at [P^].

math.AG↗

arXiv2001

Terminal 3-fold divisorial contractions of a surface to a curve, I

Let C be a smooth curve on an index 1 terminal 3-fold. We investigate the existence of extremal terminal divisorial contractions Y-->X that contract an irreducible surface E to C. We consider cases in respect to the singularities of the general hypersurface section S of X through C. We completely classify such contractions in the case that S has A_i, i < 4 and D_2n for any n, type singularities.

math.AG↗