arXiv subjects

Joseph W. Cutrone

Publications and source records attributed to Joseph W. Cutrone.

2 recordsLinked to original sources

arXiv2018

A Weak Fano Threefold Arising as a Blowup of a Curve of Genus 5 and Degree 8 on $\mathbb{P}^3$

This article constructs a smooth weak Fano threefold of Picard number two with small anti-canonical morphism that arises as a blowup of a smooth curve of genus 5 and degree 8 in $\mathbb{P}^3$. While the existence of this weak Fano was known as a numerical possibility in \cite{CM13} and constructed in BL12, this paper removes the dependencies on the results in \cite{JPR11} needed in the construction of BL12 and constructs the link in the style of ACM17.

math.AG↗

arXiv2014

Towards the Classification of Weak Fano Threefolds with ρ= 2

In this paper, we provide examples of Sarkisov links of type II between complex projective Fano threefolds $X$ with $ρ(X) = 1$. To show examples of these links, we study smooth weak Fano threefolds with extremal rays of type $E$. We further assume that the pluri-anticanonical morphism contracts only a finite number of curves. We numerically classify smooth weak Fano threefolds with $ρ(X) = 2$ having an extremal ray of type $E$ both before and after a flop as well as prove the existence of some of these numerical cases.

math.AG↗