There are finitely many rational points on a nice projective curve defined over the rationals of genus at least 2, but it is a difficult problem to explicitly determine these points. The quadratic Cha...
We prove two types of inequalities for a foliation of general type on a smooth projective surface, the slope inequality and Noether inequality, both of which provide lower bounds on the volume \(\math...
We explore the geometry of the Enriques surfaces and of the rational elliptic surfaces, particularly focusing on the genus 1 pencils they admit, on the Severi varieties of curves on them and on the ra...
I campi quadratici reali, dati dall'aggiunta a \(\mathbb{Q}\) della radice quadrata di un numero positivo che non sia lui stesso un quadrato, sono uno degli oggetti centrali della Teoria dei Numeri cl...
We will report about a jont work in progress with Ciro Ciliberto about deformations to nodal surfaces of surfaces in P^3 which are double along a line....
There are several possible generalizations of the definition of irreducible holomorphic symplectic manifold to the singular context (primitive symplectic variety, irreducible symplectic orbifold, irre...
One of the main goals of Riemannian geometry is to understand the relationship between the geometry and topology of smooth manifolds. To achieve this, it is useful to look for "canonical metrics" enco...
This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU....
We consider the cones of divisors that are ample in codimension k on a variety of dimension n, for all possible values of k. Taking closures, for k=0 and k=n-1 we obtain the pseudoeffective and the ne...
