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Equivariant compactifications of vector groups with high index
- Baohua Fu, Pedro Montero
- Mathematics
- 6 June 2018
In this note, we classify smooth equivariant compactifications of $\mathbb{G}_a^n$ which are Fano manifolds with index $\geq n-2$.
Geometry of singular Fano varieties and projective bundles over curves
- Pedro Montero
- Mathematics
- 11 October 2017
This thesis is devoted to the geometry of Fano varieties and projective vector bundles over a smooth projective curve.
In the first part we study the geometry of mildly singular Fano varieties on… Expand
On singular Fano varieties with a divisor of Picard number one
- Pedro Montero
- Mathematics
- 26 May 2016
In this paper we study the geometry of mildly singular Fano varieties on which there is an effective prime divisor of Picard number one. Afterwards, we address the case of toric varieties. Finally,… Expand
A characterization of some Fano 4-folds through conic fibrations
- Pedro Montero, E. Romano
- Mathematics
- 24 March 2018
Let $X$ be a complex projective Fano $4$-fold. Let $D\subset X$ be a prime divisor. Let us consider the image $\mathcal{N}_{1}(D,X)$ of $\mathcal{N}_{1}(D)$ in $\mathcal{N}_{1}(X)$ through the… Expand
Newton–Okounkov bodies on projective bundles over curves
- Pedro Montero
- Mathematics
- 20 March 2017
In this article, we study Newton–Okounkov bodies on projective vector bundles over curves. Inspired by Wolfe’s estimates used to compute the volume function on these varieties, we compute all… Expand
Fano Threefolds as Equivariant Compactifications of the Vector Group
- Z. Huang, Pedro Montero
- Mathematics
- 22 February 2018
In this article, we determine all equivariant compactifications of the three-dimensional vector group $\mathbf{G}_a^3$ which are smooth Fano threefolds with Picard number greater or equal than two.
Corrigendum to: A Characterization of Some Fano 4-folds Through Conic Fibrations
- Pedro Montero, E. Romano
- Mathematics
- 24 June 2020
On the liftability of the automorphism group of smooth hypersurfaces of the projective space
- V. González-Aguilera, A. Liendo, Pedro Montero
- Mathematics
- 26 April 2020
Let $X$ be a smooth hypersurface of dimension $n\geq 1$ and degree $d\geq 3$ in the projective space given as the zero set of a homogeneous form $F$. If $(n,d)\neq (1,3), (2,4)$ it is well known that… Expand