Local positivity of linear series on surfaces

We study asymptotic invariants of linear series on surfaces with the help of Newton-Okounkov polygons. Our primary aim is to understand local positivity of line bundles in terms of convex geometry. We work out characterizations of ample and nef line bundles in terms of their Newton-Okounkov bodies, treating the infinitesimal case as well. One of the main results is a description of moving Seshadri constants via infinitesimal Newton-Okounkov polygons. As an illustration of our ideas we reprove results of Ein-Lazarsfeld on Seshadri constants on surfaces

Positivity of Line Bundles and Newton-Okounkov Bodies

The purpose of this paper is to describe asymptotic base loci of line bundles on projective varieties in terms of Newton-Okounkov bodies. As a result, we obtain equivalent characterizations of ampleness and nefness via convex geometry

A Reider-type theorem for higher syzygies on abelian surfaces

Building on the theory of infinitesimal Newton-Okounkov bodies and previous work of Lazarsfeld-Pareschi-Popa, we present a Reider-type theorem for higher syzygies of ample line bundles on abelian surfaces

Okounkov bodies of finitely generated divisors

We show that the Okounkov body of a big divisor with a finitely generated section ring is a rational simplex for an appropriate choice of flag; furthermore, when the ambient variety is a surface, the same holds for every big divisor. Under somewhat more restrictive hypotheses, we also show that the corresponding semi-group is finitely generated. \ua9 2013 The Author(s)

Hazai tapasztalatok kasztrációrezisztens metasztatikus prosztatadaganatos betegek kabazitaxelterápiájával [Experience with cabazitaxel therapy for patients with metastatic castrate resistant prostate cancer in Hungary]

Our aim was to assess the efficacy and adverse effects of cabazitaxel (CBZ), a chemotherapeutic agent that can be administered to patients with metastatic castrate resistant prostate cancer (mCRPC) after docetaxel (DOC) therapy. We retrospectively analyzed data of CBZ received by mCRPC patients in 12 Hungarian oncological centers between 01/2016 and 06/2017. CBZ (25 or 20 mg/m2 q3w) was administered after DOC. Physical and laboratory examinations were performed in every cycle, tumor response was evaluated in every third cycle based on PCWG2 criteria. Adverse effects were evaluated based on CTCAE 4.0. Data of 60 patients were analyzed. CBZ was administered in 2nd and 3rd lines in 31.6% and 46.6%, while in 4th and 5th lines in 15% and 6.6% patients, respectively. Its starting dose was 25 mg/m2 and 20 mg/m2 in 65% and 35% of cases, respectively. The median number of cycles was 5. Progression-free survival and overall survival were 5.52 and 15.77 months, respectively. Survival results were similar in case of DOC-CBZ-ART/alfaradin and DOC-ART/alfaradin-CBZ sequences. Adverse effects were detected in 63,3% of patients. The most common adverse effects were neutropenia, anemia, and diarrhea. Our observations suggest that CBZ, with the appropriate support and chemotherapeutic experience, is well-tolerated and effective therapy of mCRPC after DOC

Recent developments and open problems in linear series

In the week of October 3–9, 2010, the Mathematisches Forschungsinstitut at Oberwolfach hosted the Mini-Workshop “Linear Series on Algebraic Varieties.” These notes contain a variety of interesting problems which motivated the participants prior to the event, and examples, results and further problems which grew out of discussions during and shortly after the workshop. Many arguments presented here are scattered in the literature or constitute “folklore.” It was one of our aims to have a usable and easily accessible collection of examples and results

Geographical differences in the management of metastatic de novo renal cell carcinoma in the era of immune-combinations

BACKGROUND: The upfront treatment of metastatic renal cell carcinoma (mRCC) has been revolutionized by the in-troduction of immune-based combinations. The role of cytoreductive nephrectomy (CN) in these patients is still debated. The ARON-1 study (NCT05287464) was designed to globally analyze real-world data of mRCC patients receiving first -line immuno-oncology combinations. This sub-analysis is focused on the role of upfront or delayed partial or radical CN in three geographical areas (Western Europe, Eastern Europe, America/Asia).METHODS: We conducted a multicenter retrospective observational study in mRCC patients treated with first-line im-mune combinations from 55 centers in 19 countries. From 1152 patients in the ARON-1 dataset, we selected 651 patients with de novo mRCC. 255 patients (39%) had undergone CN, partial in 14% and radical in 86% of cases; 396 patients (61%) received first-line immune-combinations without previous nephrectomy.RESULTS: Median overall survival (OS) from the diagnosis of de novo mRCC was 41.6 months and not reached (NR) in the CN subgroup and 24.0 months in the no CN subgroup, respectively (P<0.001). Median OS from the start of first -line therapy was NR in patients who underwent CN and 22.4 months in the no CN subgroup (P<0.001). Patients who underwent CN reported longer OS compared to no CN in all the three geographical areas.CONCLUSIONS: No significant differences in terms of patients' outcome seem to clearly emerge, even if the rate CN and the choice of the type of first-line immune-based combination varies across the different Cancer Centers participating in the ARON-1 project