Embedded desingularization of toric varieties

We present a new method to achieve an embedded desingularization of a toric variety. Let $W$ be a regular toric variety defined by a fan $\Sigma$ and $X\subset W$ be a toric embedding. We construct a finite sequence of combinatorial blowing-ups such that the final strict transforms $X'\subset W'$ are regular and $X'$ has normal crossing with the exceptional divisor.Comment: Some comments have been corrected and references adde

Dynamical transitions in a pollination--herbivory interaction

Plant-pollinator associations are often seen as purely mutualistic, while in reality they can be more complex. Indeed they may also display a diverse array of antagonistic interactions, such as competition and victim--exploiter interactions. In some cases mutualistic and antagonistic interactions are carried-out by the same species but at different life-stages. As a consequence, population structure affects the balance of inter-specific associations, a topic that is receiving increased attention. In this paper, we developed a model that captures the basic features of the interaction between a flowering plant and an insect with a larval stage that feeds on the plant's vegetative tissues (e.g. leaves) and an adult pollinator stage. Our model is able to display a rich set of dynamics, the most remarkable of which involves victim--exploiter oscillations that allow plants to attain abundances above their carrying capacities, and the periodic alternation between states dominated by mutualism or antagonism. Our study indicates that changes in the insect's life cycle can modify the balance between mutualism and antagonism, causing important qualitative changes in the interaction dynamics. These changes in the life cycle could be caused by a variety of external drivers, such as temperature, plant nutrients, pesticides and changes in the diet of adult pollinators. Abstract Keywords: mutualism, pollination, herbivory, insects, stage-structure, oscillationsComment: 20 pages, 7 main figures, 2 appendix figure