arXiv subjects

C. Folegatti

Publications and source records attributed to C. Folegatti.

2 recordsLinked to original sources

arXiv2004

On a special class of smooth codimension two subvarieties in $\mathbb{P}^n$, $n \geq 5$

We consider smooth codimension two subcanonical subvarieties in $\mathbb{P}^n$ with $n \geq 5$, lying on a hypersurface of degree $s$ having a linear subspace of multiplicity $(s-2)$. We prove that such varieties are complete intersections. We also give a little improvement to some earlier results on the non existence of rank two vector bundles on $\mathbb{P}^4$ with small Chern classes.

math.AG↗

arXiv2004

On smooth surfaces in P4 containing a plane curve

We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ and prove some general result concerning the linear system $|H-P|$. We then look at regular surfaces lying on hypersurfaces of degree $s$ having a plane of multiplicity $(s-2)$. This implies that $S$ contains a plane curve. We prove that the degree of such surfaces is bounded and for $s=4$ we compute an actual bound.

math.AG↗