Jacobian of meromorphic curves

The contact structure of two meromorphic curves gives a factorization of their jacobian.Comment: 41 pages, amstex, to be published in the Proceedings of the Indian Academy of Science

On curves with one place at infinity

Let $f$ be a plane curve. We give a procedure based on Abhyankar's approximate roots to detect if it has a single place at infinity, and if so construct its associated $\delta$-sequence, and consequently its value semigroup. Also for fixed genus (equivalently Frobenius number) we construct all $\delta$-sequences generating numerical semigroups with this given genus. For a $\delta$-sequence we present a procedure to construct all curves having this associated sequence. We also study the embeddings of such curves in the plane. In particular, we prove that polynomial curves might not have a unique embedding.Comment: 14 pages, 2 figure

Irreducibility criterion for quasi-ordinary polynomials

Using the notion of approximate roots and that of generalized Newton sets, we give a local criterion for a quasi ordinary polynomial to be irreducible. Such a criterion is useful in the study of singularities of quasi-ordinary hypersurfaces. It generalizes the criterion given by S.S. Abhyankar for algebraic plane curves

The Frobenius Vector of a Free Affine Semigroup

We give a formula for the Frobenius vector of a free affine simplicial semigroup. This generalizes to the affine case a well known formula for free numerical semigroup

Development of thrombocytopenia is associated with improved survival in patients treated with immunotherapy

Background: Immune-related adverse events are associated with efficacy of immune checkpoint inhibitors (ICIs). We hypothesize that immune-mediated thrombocytopenia could be a biomarker for response to ICIs. Materials & methods: This retrospective study included 215 patients with metastatic malignancies treated with ICIs. Patients were stratified by nadir platelet count. Outcomes of interest were progression-free survival and overall survival. Results: On multivariate analysis, grade 1 thrombocytopenia was positively associated with overall survival compared with patients who did not develop thrombocytopenia (hazard ratio [HR]= 0.28 [95% CI: 0.13–0.60]; p = 0.001), while grade 2–4 thrombocytopenia was not (HR= 0.36 [95% CI: 0.13–1.04]; p = 0.060). There was no association between degree of thrombocytopenia and progression-free survival. Conclusion: Follow-up studies are warranted to substantiate the predictive significance of thrombocytopenia in patients receiving ICIs

Worldsheet Realization of the Refined Topological String

A worldsheet realization of the refined topological string is proposed in terms of physical string amplitudes that compute generalized N=2 F-terms of the form F_{g,n} W^{2g}Y^{2n} in the effective supergravity action. These terms involve the chiral Weyl superfield W and a superfield Y defined as an N=2 chiral projection of a particular anti-chiral T-bar vector multiplet. In Heterotic and Type I theories, obtained upon compactification on the six-dimensional manifold K3xT2, T is the usual K\"ahler modulus of the T2 torus. These amplitudes are computed exactly at the one-loop level in string theory. They are shown to reproduce the correct perturbative part of the Nekrasov partition function in the field theory limit when expanded around an SU(2) enhancement point of the string moduli space. The two deformation parameters epsilon_- and epsilon_+ of the Omega-supergravity background are then identified with the constant field-strength backgrounds for the anti-self-dual graviphoton and self-dual gauge field of the T-bar vector multiplet, respectively.Comment: 35 pages, typos corrected, published in NP