Poster Session

LIST OF POSTERS

In this poster, I will present an extension for toric geometry of the logarithmic tangent sheaf. Then I will provide a connection of this sheaf to the theory of distributions and finally, I will show a criterion, for one homogeneous polynomial, to decide when the extended logarithmic tangent sheaf is free which classically is known as the Saito’s criterion.  This is a joint work in progress with Daniele Faenzi and Marcos Jardim. 

On a smooth projective curve the locus of stable bundles that remain stable on all etale Galois covers prime to the characteristic defines a big open in the moduli space of stable bundles. In particular, the bundles trivialized on some etale Galois cover of degree prime to the characteristic are not dense - in contrast to a theorem of Ducrohet and Mehta stating that all etale trivializable bundles are dense in positive characteristic. As an application we study the closure of the prime to p etale trivializable vector bundles. This closure is closely related to a stratification of the moduli space of stable vector bundles via their decomposition behaviour on Galois covers of degree prime to the characterstic. We obtain mostly sharp dimension estimates for the closure of the prime to p etale trivializable bundles as well as the decomposition strata.