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Equivariant compactifications of vector groups with high index
In this note, we classify smooth equivariant compactifications of $\mathbb{G}_a^n$ which are Fano manifolds with index $\geq n-2$.
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Geometry of singular Fano varieties and projective bundles over curves
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 onExpand
On singular Fano varieties with a divisor of Picard number one
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
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A characterization of some Fano 4-folds through conic fibrations
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 theExpand
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Newton–Okounkov bodies on projective bundles over curves
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 allExpand
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Fano Threefolds as Equivariant Compactifications of the Vector Group
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.
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On the liftability of the automorphism group of smooth hypersurfaces of the projective space
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 thatExpand
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