arXiv subjects

Vincenzo Ancona

Publications and source records attributed to Vincenzo Ancona.

2 recordsLinked to original sources

arXiv2000

On the quantum cohomology of Fano bundles over projective spaces

In their paper "Quantum cohomology of projective bundles over $P^n$" (Trans. Am. Math. Soc. (1998)350:9 3615-3638) Z.Qin and Y.Ruan introduce interesting techniques for the computation of the quantum ring of manifolds which are projectivized bundles over projective spaces; in particular, in the case of splitting bundles they prove under some restrictions the formula of Batyrev about the quantum ring of toric manifolds. Here we prove the formula of Batyrev on the quantum Chern-Leray equation for a large class of splitting bundles.

math.AG↗

arXiv1995

On singularities of ${\cal M}_{I\!\! P^3}(c_1,c_2)$

Let ${\cal M}_{I\!\! P^3}(c_1,c_2)$ be the moduli space of stable rank-$2$ vector bundles on $I\!\! P^3$ with Chern classes $c_1$, $ c_2$. We prove the following results. 1) Let $0 \le β< γ$ be two integers, ($γ\ge 2)$, such that $2γ-3β>0$; then ${\cal M}_{I\!\! P^3}(0,2γ^2-3β^2)$ is singular (the case $β=0$ was previously proved by M. Maggesi). 2) Let $0 \le β< γ$ be two odd integers ($γ\ge 5)$, such that $2γ-3β+1>0$; then ${\cal M}_{I\!\! P^3}(-1,2(γ/2)^2-3(β/2)^2+1/4)$ is singular. In particular ${\cal M}_{I\!\! P^3}(0,5)$, ${\cal M}_{I\!\! P^3}(-1,6)$ are singular.

alg-geom↗