Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)

In this paper, we formulate the geometric Bogomolov conjecture for abelian varieties, and give some partial answers to it. In fact, we insist in a main theorem that under some degeneracy condition, a closed subvariety of an abelian variety does not have a dense subset of small points if it is a non-special subvariety. The key of the proof is the study of the minimal dimension of the components of a canonical measure on the tropicalization of the closed subvariety. Then we can apply the tropical version of equidistribution theory due to Gubler. This article includes an appendix by Walter Gubler. He shows that the minimal dimension of the components of a canonical measure is equal to the dimension of the abelian part of the subvariety. We can apply this result to make a further contribution to the geometric Bogomolov conjecture.Comment: 30 page

On symplectic quotients of K3 surfaces

In this note, we construct generalized Shioda-Inose structures on K3 surfaces using cyclic covers and almost functoriality of Shioda-Inose structures with respect to normal subgroups of a given group of symplectic automorphisms

Non-urothelial bladder cancer: comparison of clinicopathological and prognostic characteristics in pure adenocarcinoma and non-bilharzial squamous cell carcinoma of the bladder

Objectives: The clinicopathological characteristics, treatment modalities, and effects on the prognosis of pure squamous cell carcinoma (SqCC) and adenocarcinoma (AC) were evaluated. Materials and Methods: 86 patients with pure SqCC and AC bladder cancer were evaluated retrospectively. Results: Of the 86 patients, 51 had SqCC and 35 had AC. No differences in clinicopathological characteristics were observed between patients with AC and SqCC, except for the prevalence of T4 disease (28.6% vs. 51.0%, respectively). In multivariate analysis, older age, stage IV disease, and Eastern Cooperative Oncology Group (ECOG) performance status (> 2) were predictive of a poor overall survival (OS). The median OS was significantly longer for stage I-III patients (82.9 months) treated with surgery ± chemotherapy (CT) ± radiotherapy (RT) than for those treated with transurethral resection ± CT ± RT (24.3 months) (P = 0.007). The median OS of patients with SqCC and AC who were given platinum-based CT for metastasis was 7.7 and 30.3 months, respectively. Conclusions: Advanced age, stage IV disease, and poor ECOG performance status were factors associated with a poor prognosis. Surgery ± CT ± RT resulted in significantly better OS, except in stage IV disease. Patients with metastatic AC had better response rates with platinum- based CT. © 2018 S. Karger GmbH, Freiburg

Squamous Cell Carcinoma of the Bladder

Objectives: The clinicopathological characteristics, treatment modalities, and effects on the prognosis of pure squamous cell carcinoma (SqCC) and adenocarcinoma (AC) were evaluated. Materials and Methods: 86 patients with pure SqCC and AC bladder cancer were evaluated retrospectively. Results: Of the 86 patients, 51 had SqCC and 35 had AC. No differences in clinicopathological characteristics were observed between patients with AC and SqCC, except for the prevalence of T4 disease (28.6% vs. 51.0%, respectively). In multivariate analysis, older age, stage IV disease, and Eastern Cooperative Oncology Group (ECOG) performance status (> 2) were predictive of a poor overall survival (OS). The median OS was significantly longer for stage I-III patients (82.9 months) treated with surgery +/- chemotherapy (CT) +/- radiotherapy (RT) than for those treated with transurethral resection +/- CT +/- RT (24.3 months) (P = 0.007). The median OS of patients with SqCC and AC who were given platinum-based CT for metastasis was 7.7 and 30.3 months, respectively. Conclusions: Advanced age, stage IV disease, and poor ECOG performance status were factors associated with a poor prognosis. Surgery +/- CT +/- RT resulted in significantly better OS, except in stage IV disease. Patients with metastatic AC had better response rates with platinum- based CT. (c) 2018 S. Karger GmbH, Freibur