arXiv subjects

Michele Nicolussi

Publications and source records attributed to Michele Nicolussi.

3 recordsLinked to original sources

arXiv2018

On terminal Fano 3-folds with 2-torus action

We classify the terminal Fano threefolds of Picard number one that come with an effective action of a two-torus. Our approach applies also to higher dimensions and generalizes the correspondence between toric Fano varieties and lattice polytopes: to any Fano variety with a complete intersection Cox ring we associate its "anti canonical complex", which is a certain polyhedral complex living in the lattice of one parameter groups of an ambient toric variety. For resolutions constructed via the tropical variety, the lattice points inside the anticanonical complex control the discrepancies. This leads, for example, to simple characterizations of terminality and canonicity.

math.AG↗

arXiv2018

On terminal Fano 3-folds with 2-torus action, part II

We continue the classification of terminal Fano threefolds with an effective two-torus action. In earlier work we settled the Q-factorial case with Picard number one. Here we treat the larger class of varieties that do not admit any contraction of a prime divisor; these are called combinatorially minimal.

math.AG↗

arXiv2016

Smooth projective varieties with a torus action of complexity 1 and Picard number 2

We give an explicit description of all smooth varieties with a torus action of complexity one having Picard number at most two. As a consequence, we classify in every dimension the smooth (almost) Fano varieties with a torus action of complexity one having Picard number two. It turns out that all the Fano examples are obtained via an iterated generalized cone construction from a series of smooth varieties of dimension at most seven.

math.AG↗