On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces

We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor correction

Remarks on hard Lefschetz conjectures on Chow groups

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.Comment: to appear in Sciences in China, Ser. A Mathematic

Varieties of vacua in classical supersymmetric gauge theories

We give a simple description of the classical moduli space of vacua for supersymmetric gauge theories with or without a superpotential. The key ingredient in our analysis is the observation that the lagrangian is invariant under the action of the complexified gauge group \Gc. From this point of view the usual $D$-flatness conditions are an artifact of Wess--Zumino gauge. By using a gauge that preserves \Gc invariance we show that every constant matter field configuration that extremizes the superpotential is \Gc gauge-equivalent (in a sense that we make precise) to a unique classical vacuum. This result is used to prove that in the absence of a superpotential the classical moduli space is the algebraic variety described by the set of all holomorphic gauge-invariant polynomials. When a superpotential is present, we show that the classical moduli space is a variety defined by imposing additional relations on the holomorphic polynomials. Many of these points are already contained in the existing literature. The main contribution of the present work is that we give a careful and self-contained treatment of limit points and singularities.Comment: 14 pages, LaTeX (uses revtex.sty

Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

Fibrations on four-folds with trivial canonical bundles

Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and prove that there is no such fibration in the sixth class. We classify all such fibrations whose generic fibre is the Jacobian of a genus two curve.Comment: 28 page

Five-year study assessing the clinical utility of anti-Müllerian hormone measurements in reproductive-age women with cancer

An important discussion point before chemotherapy is ovarian toxicity, a side-effect that profoundly affects young women with cancer. Their quality of life after successful treatment, including the ability to conceive, is a major concern. We asked whether serum anti-Müllerian hormone (AMH) measurements before chemotherapy for two most common malignancies are predictive of long-term changes in ovarian reserve? A prospective cohort study measured serum AMH in 66 young women with lymphoma and breast cancer, before and at 1 year and 5 years after chemotherapy, compared with 124 healthy volunteers of the same age range (18-43 years). Contemporaneously, patients reported their menses and live births during 5-year follow-up. After adjustment for age, serum AMH was 1.4 times higher (95% CI 1.1 to 1.9; P < 0.02) in healthy volunteers than in cancer patients before chemotherapy. A strong correlation was observed between baseline and 5-year AMH in the breast cancer group (P < 0.001, regression coefficient = 0.58, 95% CI 0.29 to 0.89). No significant association was found between presence of menses at 5 years and serum AMH at baseline (likelihood ratio test from logistics regression analysis). Reproductive-age women with malignancy have lower serum AMH than healthy controls even before starting chemotherapy. Pre-chemotherapy AMH was significantly associated with long-term ovarian function in women with breast cancer. At key time points, AMH measurements could be used as a reproductive health advisory tool for young women with cancer. Our results highlight the unsuitability of return of menstruation as a clinical indicator of ovarian reserve after chemotherapy. [Abstract copyright: Crown Copyright © 2019. Published by Elsevier Ltd. All rights reserved.

Stability conditions and positivity of invariants of fibrations

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthda

Generating multimedia presentations: from plain text to screenplay

In many Natural Language Generation (NLG) applications, the output is limited to plain text – i.e., a string of words with punctuation and paragraph breaks, but no indications for layout, or pictures, or dialogue. In several projects, we have begun to explore NLG applications in which these extra media are brought into play. This paper gives an informal account of what we have learned. For coherence, we focus on the domain of patient information leaflets, and follow an example in which the same content is expressed first in plain text, then in formatted text, then in text with pictures, and finally in a dialogue script that can be performed by two animated agents. We show how the same meaning can be mapped to realisation patterns in different media, and how the expanded options for expressing meaning are related to the perceived style and tone of the presentation. Throughout, we stress that the extra media are not simple added to plain text, but integrated with it: thus the use of formatting, or pictures, or dialogue, may require radical rewording of the text itself

The Moduli of Reducible Vector Bundles

A procedure for computing the dimensions of the moduli spaces of reducible, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds X is presented. This procedure is applied to poly-stable rank n+m bundles of the form V + pi* M, where V is a stable vector bundle with structure group SU(n) on X and M is a stable vector bundle with structure group SU(m) on the base surface B of X. Such bundles arise from small instanton transitions involving five-branes wrapped on fibers of the elliptic fibration. The structure and physical meaning of these transitions are discussed.Comment: 33+1 page

Calorons, Nahm's equations on S^1 and bundles over P^1xP^1

The moduli space of solutions to Nahm's equations of rank (k,k+j) on the circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit matrix description of these spaces is given by a monad constructio