Francesco Zucconi

Graded rings of rank 2 Sarkisov links

We compute a class of Sarkisov links from Fano 3-folds embedded in weighted Grassmannians using explicit methods for describing graded rings associated to a variation of geometric invariant theory (GIT) quotient.

Numerical inequalities for surfaces with canonical map composed with a pencil

Abstract In this paper we solve the problem proposed by Xiao about the existence of surfaces with p g = 4, K 2 X = 9 and canonical map composed with a pencil [X4]. In fact we show that such surfaces do not exist. As a consequence of our non-existence result we obtain the new bound K 2 X ≥ 4 p g − 6 where X is a minimal surface of general type with canonical map composed with a pencil and p g ( X ) ≥ 3.

Circle of Sarkisov links on a Fano 3-fold

For a general Fano

Gonality, apolarity and hypercubics

3

FERMAT HYPERSURFACES AND SUBCANONICAL CURVES

-fold of index

Generalized hyperelliptic surfaces

1

Generalized adjoint forms on algebraic varieties

in the weighted projective space

On subcanonical Gorenstein varieties and apolarity

\mathbb{P}(1,1,1,1,2,2,3)

ABELIAN COVERS AND ISOTRIVIAL CANONICAL FIBRATIONS

we construct

Birational Geometry of 3-fold Mori Fibre Spaces

2