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Carla Novelli

Publications and source records attributed to Carla Novelli.

11 recordsLinked to original sources
arXiv2026

Numerical tropical line bundles and toric b-divisors

We study the relationship between line bundles on tropical compactifications of a very affine variety $Y$ and toric b-divisors on the associated tropical variety ${\rm Trop}(Y)$. By focusing on numerical equivalence classes, we construct a natural injective map from the group of numerical tropical line bundles on $Y$ to the space of toric b-divisors modulo linear equivalence. Moreover, we show that this map restricts to a bijection between the tropical nef cone of $Y$ and the set of toric b-divisors that are b-Cartier and tropically nef. This provides a higher-dimensional generalization of Baker's specialization for curves and clarifies the birational nature of tropical line bundles. We also discuss the kernel of the map from line bundles to numerical tropical line bundles, which encodes the continuous moduli lost in tropicalization.

math.AG↗
arXiv2023

Triple solids and scrolls

Let $Y$ be a smooth projective variety of dimension $n \geq 2$ endowed with a finite morphism $ϕ:Y \to \mathbb P^n$ of degree $3$, and suppose that $Y$, polarized by some ample line bundle, is a scroll over a smooth variety $X$ of dimension $m$. Then $n \leq 3$ and either $m=1$ or $2$. When $m=1$, a complete description of the few varieties $Y$ satisfying these conditions is provided. When $m=2$, various restrictions are discussed showing that in several instances the possibilities for such a $Y$ reduce to the single case of the Segre product $\mathbb P^2 \times \mathbb P^1$. This happens, in particular, if $Y$ is a Fano threefold as well as if the base surface $X$ is $\mathbb P^2$.

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arXiv2017

Mori contractions of maximal length

We prove a relative version of the theorem of Cho, Miyaoka and Shepherd-Barron: a Mori fibre space of maximal length is birational to a projective bundle.

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arXiv2017

Fano varieties with small non-klt locus

Let X be a Fano variety of index k such that the non-klt locus Nklt(X) is not empty. We prove that Nklt(X) has dimension at least k-1 and equality holds if and only if Nklt(X) is a linear projective space P^{k-1}. In this case X has lc singularities and is a generalised cone with Nklt(X) as vertex. If X has lc singularities and Nklt(X) has dimension k we describe the non-klt locus and the global geometry of X. Moreover, we construct examples to show that all the classification results are effective.

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arXiv2011

On Fano manifolds with an unsplit dominating family of rational curves

We study Fano manifolds $X$ admitting an unsplit dominating family of rational curves and we prove that the Generalized Mukai Conjecture holds if $X$ has pseudoindex $i_X = (\dim X)/3$ or dimension $\dim X=6$. We also show that this conjecture is true for all Fano manifolds with $i_X > (\dim X)/3$.

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arXiv2011

Extremal rays of non-integral $L$-length

Let $X$ be a smooth complex projective variety and let $L$ be a line bundle on it. We describe the structure of the pre-polarized manifold $(X,L)$ for non integral values of the invariant $τ_L(R):=-K_X\cdotΓ/(L \cdot Γ)$, where $Γ$ is a minimal curve of an extremal ray $R:=\mathbb R_+[Γ]$ on $X$ such that $L \cdot R>0$.

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arXiv2011

Geometry of rays-positive manifolds

Let M be a smooth complex projective variety and let L be a line bundle on it. Rays-positive manifolds, namely pairs (M,L) such that L is numerically effective and L\cdotR > 0 for all extremal rays R on M, are studied. Several illustrative examples and some applications are provided. In particular, projective varieties with crepant singularities and of small degree with respect to the codimension are classified, and the non-negativity of the sectional genus g(M,L) is proven, describing as well the pairs with g(M,L) = 0,1.

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arXiv2010

Manifolds covered by lines and extremal rays

Let $X$ be a smooth complex projective variety and let $H \in \pic(X)$ be an ample line bundle. Assume that $X$ is covered by rational curves with degree one with respect to $H$ and with anticanonical degree greater than or equal to $(\dim X -1)/2$. We prove that there is a covering family of such curves whose numerical class spans an extremal ray in the cone of curves $\cone(X)$.

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