An inclusion result for dagger closure in certain section rings of abelian varieties

We prove an inclusion result for graded dagger closure for primary ideals in symmetric section rings of abelian varieties over an algebraically closed field of arbitrary characteristic.Comment: 11 pages, v2: updated one reference, fixed 2 typos; final versio

Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

The role of adjuvant chemotherapy for patients with resected pancreatic cancer: Systematic review of randomized controlled trials and meta-analysis

Background: In patients undergoing surgery for resectable pancreatic cancer prognosis still remains poor. The role of adjuvant treatment strategies (including chemotherapy and chemoradiotherapy) following resection of pancreatic cancer remains controversial. Methods: A Medline-based literature search was undertaken to identify randomized controlled trials that evaluated adjuvant chemotherapy after complete macroscopic resection for cancer of the exocrine pancreas. Five trials of adjuvant chemotherapy were eligible and critically reviewed for this article. A meta-analysis (based on published data) was performed with survival (median survival time and 5-year survival rate) being the primary endpoint. Results: For the meta-analysis, 482 patients were allocated to the chemotherapy group and 469 patients to the control group. The meta-analysis estimate for prolongation of median survival time for patients in the chemotherapy group was 3 months (95% CI 0.3-5.7 months, p = 0.03). The difference in 5-year survival rate was estimated with 3.1% between the chemotherapy and the control group (95% CI -4.6 to 10.8%, p > 10.05). Conclusion: Currently available data from randomized trials indicate that adjuvant chemotherapy after resection of pancreatic cancer may substantially prolong disease-free survival and cause a moderate increase in overall survival. In the current meta-analysis, a significant survival benefit was only seen with regard to median survival, but not for the 5-year survival rate. The optimal chemotherapy regimen in the adjuvant setting as well as individualized treatment strategies (also including modern chemoradiotherapy regimens) still remain to be defined. Copyright (C) 2008 S. Karger AG, Basel

Multivariate Poincar\'e series for algebras of SL2SL_2-invariants

Let \mathcal{C}_{\mathbi{d}}, \mathcal{I}_{\mathbi{d}}, \mathbi{d}{=}(d_1,d_2,..., d_n) be the algebras of join covariants and joint invariants of the $n$ binary forms of degrees $d_1,d_2,..., d_n.$ Formulas for computation of the multivariate Poincar\'e series \mathcal{P}(\mathcal{C}_{\mathbi{d}},z_1,z_2,...,z_n,t) and \mathcal{P}(\mathcal{I}_{\mathbi{d}},z_1,z_2,...,z_n) are found.Comment: 5 page

The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co

Phase III Prospective Randomized Comparison Trial of Depot Octreotide Plus Interferon Alfa-2b Versus Depot Octreotide Plus Bevacizumab in Patients With Advanced Carcinoid Tumors: SWOG S0518

Purpose Treatment options for neuroendocrine tumors (NETs) remain limited. This trial assessed the progression-free survival (PFS) of bevacizumab or interferon alfa-2b (IFN-α-2b) added to octreotide among patients with advanced NETs. Patients and Methods Southwest Oncology Group (SWOG) S0518, a phase III study conducted in a US cooperative group system, enrolled patients with advanced grades 1 and 2 NETs with progressive disease or other poor prognostic features. Patients were randomly assigned to treatment with octreotide LAR 20 mg every 21 days with either bevacizumab 15 mg/kg every 21 days or 5 million units of IFN-α-2b three times per week. The primary end point was centrally assessed PFS. This trial is registered with ClinicalTrials.gov as NCT00569127. Results A total of 427 patients was enrolled, of whom 214 were allocated to bevacizumab and 213 to IFN-α-2b. The median PFS by central review was 16.6 months (95% CI, 12.9 to 19.6 months) in the bevacizumab arm and was 15.4 months (95% CI, 9.6 to 18.6 months) in the IFN arm (hazard ratio [HR], 0.93; 95% CI, 0.73 to 1.18; P = .55). By site review, the median PFS times were 15.4 months (95% CI, 12.6 to 17.2 months) for bevacizumab and 10.6 months (95% CI, 8.5 to 14.4 months) for interferon (HR, 0.90; 95% CI, 0.72 to 1.12; P = .33). Time to treatment failure was longer with bevacizumab than with IFN (HR, 0.72; 95% CI, 0.58 to 0.89; P = .003). Confirmed radiologic response rates were 12% (95% CI, 8% to 18%) for bevacizumab and 4% (95% CI, 2% to 8%) for IFN. Common adverse events with bevacizumab and octreotide included hypertension (32%), proteinuria (9%), and fatigue (7%); with IFN and octreotide, they included fatigue (27%), neutropenia (12%), and nausea (6%). Conclusion No significant differences in PFS were observed between the bevacizumab and IFN arms, which suggests that these agents have similar antitumor activity among patients with advanced NETs

Economic evaluation of rituximab plus cyclophosphamide, vincristine and prednisolone for advanced follicular lymphoma

The addition of rituximab to cyclophosphamide, vincristine and prednisolone (CVP) for advanced follicular lymphoma increases median time to progression by 17 months. A US societal cost-effectiveness of R-CVP versus CVP is estimated for a representative 50-year-old patient. Progression-free survival (PFS) and overall survival are based on a randomized Phase III trial. Costs are estimated using Medicare reimbursement rates and published drug price data, and include drug and administration costs, adverse events, treatment of relapses, and end-of-life care. Utility estimates are derived from the literature and a 3% discount rate is employed. Mean overall survival is projected to be 1.51 years longer for patients assigned to R-CVP versus CVP. The cost per quality-adjusted year of life gained is $28,565. The utility associated with stable or progressive disease and the unit drug cost of rituximab most influence the findings. The cost-effectiveness ratio of R-CVP compared with CVP is projected to be cost-effective in the United States under a range of sensitivity analyses

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio