arXiv subjects
Publications and source records attributed to Anna Lekontseva.
We study surjective (not necessarily regular) rational endomorphisms $f$ of smooth del Pezzo surfaces $X$. We prove that under certain natural non\,-\,degeneracy condition $f$ can have degree bigger than $1$ only when $(-K_X^2) > 5$. Some structural properties of $f$ in the case $X = \p^2$ are also established.
Prokaryotes have evolved various mechanisms to counter viruses, which in their turn developed numerous strategies to avoid defenses of the hosts. Dozens of such defense and counter-defense mechanisms have recently been discovered, yet the number of such systems held by a given virus or its host is limited. Here, we present numerical and theoretical arguments for the existence of the maximal number of ecologically and evolutionary sustainable defense and counter-defense systems maintained by both sides at any time of the never-ending evolutionary arms race. We find that the number of such systems is of the order of 10 for a broad range of assumptions about the costs and benefits of defense and counter-defense mechanisms and their specificity. This optimum in the number of defense and counter-defense systems appears as a result of a compromise between the metabolic and autoimmune costs of adding a new layer of defense and the benefits it conveys.