Ever since the arrival of the tomato to Spain in the 16th century, great diversification of the crop has taken place, giving rise to a rich collection of varietal types. The ‘Comunidad Valenciana’, with its deep-rooted agricultural tradition, is one of the Spanish regions with the greatest diversity in traditional tomato varieties, characterised by their local adaptation and high fruit quality....

We define relative support varieties with respect to some fixed module over a finite dimensional algebra. These varieties share many of the standard properties of classical support varieties. Moreover, when introducing finite generation conditions on cohomology, we show that relative support varieties contain homological information on the modules involved. As an application, we provide a new c...

The symmetric projective varieties of rank one are all smooth and Fano by a classic result of Akhiezer. We classify the locally factorial (respectively smooth) projective symmetric G-varieties of rank 2 which are Fano. When G is semisimple we classify also the locally factorial (respectively smooth) projective symmetric G-varieties of rank 2 which are only quasi-Fano. Moreover, we classify the ...

Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover classical geometric objects, such as toric and determinantal varieties and their secant varieties, but larger trees lead to new and largely unexplored territory...

We study (weak) log abelian varieties with constant degeneration in the log flat topology. If the base is a log point, we further study the endomorphism algebras of log abelian varieties. In particular, we prove the dual short exact sequence for isogenies, Poincaré complete reducibility theorem for log abelian varieties, and the semisimplicity of the endomorphism algebras of log abelian varieti...

In the setting of strict wonderful varieties we answer positively to Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits or model spaces. To make the paper self-contained as much as possible, we sha...