Given a curve of genus 3 with an unramified double cover, we give an explicit description of the associated Prym variety. We also describe how an unramified double cover of a non-hyperelliptic genus 3 curve can be mapped into the Jacobian of a curve of genus 2 over its field of definition and how this can be used to do Chabautyand Brauer-Manin type calculations for curves of genus 5 with an unr...

If X is a smooth projective toric variety of dimension n we give explicit conditions on characters of the torus giving an embedding X →֒ Pr that guarantee dimSecX = 2n+ 1. We also give necessary and sufficient conditions for a general point of SecX to lie on a unique secant line when X is embedded into Pr using a complete linear system. For X of dimension 2 and 3 we give formulas for deg SecX in...

Richardson varieties play an important role in intersection theory and in the geometric interpretation of the Littlewood-Richardson Rule for flag varieties. We discuss three natural generalizations of Richardson varieties which we call projection varieties, intersection varieties, and rank varieties. In many ways, these varieties are more fundamental than Richardson varieties and are more easil...

We study a family of subvarieties of the flag variety defined by certain linear conditions, called Hessenberg varieties. We compare them to Schubert varieties. We prove that some Schubert varieties can be realized as Hessenberg varieties and vice versa. Our proof explicitly identifies these Schubert varieties by their permutation and computes their dimension. We use this to answer an open quest...

Proposing the similarity measures formula between Vague sets E and G. Concluding Vague resistance analysis. The concrete application steps were:1Establishing comprehensive characters set; 2Screening excellent varieties set; 3Extracting theory optimal varieties set; 4The single-value date transformed into Vague date, obtaining different varieties Vague sets; 5Vague resistance analysis 1,the simi...

In this paper, a characterization of the language varieties and congruence varieties corresponding to M -solid pseudovarieties is presented. Taking into account the isomorphisms of the Eilenberg-type correspondences, each complete sublattice of pseudovarieties corresponds to a complete sublattice of language varieties, as well as another one of congruence varieties. For the varieties of tree la...

In this paper, a characterization of the language varieties and congruence varieties corresponding toM -solid pseudovarieties is presented. Taking into account the isomorphisms of the Eilenberg-type correspondences, each complete sublattice of pseudovarieties corresponds to a complete sublattice of language varieties, as well as another one of congruence varieties. For the varieties of tree lan...