Hamid Ahmadinezhad

On pliability of del Pezzo fibrations and Cox rings

We develop some concrete methods to build Sarkisov links, starting from Mori fibre spaces. This is done by studying low rank Cox rings and their properties. As part of this development, we give an algorithm to construct explicitly the coarse moduli space of a toric Deligne-Mumford stack. This can be viewed as the generalisation of the notion of well-formedness for weighted projective spaces to homogeneous coordinate ring of toric varieties. As an illustration, we apply these methods to study birational transformations of certain fibrations of del Pezzo surfaces over

Circle of Sarkisov links on a Fano 3-fold

\mathbb{P}^1

Non-rigid quartic 3-folds

, into other Mori fibre spaces, using Cox rings and variation of geometric invariant theory. We show that the pliability of these Mori fibre spaces is at least three and they are not rational.

On del Pezzo fibrations that are not birationally rigid

For a general Fano

Geometric aspects of robust testing for normality and sphericity

3

On conjugacy classes of the Klein simple group in Cremona group

-fold of index

SINGULAR DEL PEZZO FIBRATIONS AND BIRATIONAL RIGIDITY

1

Mori dream spaces and birational rigidity of Fano 3-folds

in the weighted projective space

Stable rationality of higher dimensional conic bundles

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

An algebraic study of linkages with helical joints

we construct