A Lie algebra attached to a projective variety

Each choice of a K\"ahler class on a compact complex manifold defines an action of the Lie algebra \slt on its total complex cohomology. If a nonempty set of such K\"ahler classes is given, then we prove that the corresponding \slt-copies generate a semisimple Lie algebra. We investigate the formal properties of the resulting representation and we work things out explicitly in the case of complex tori, hyperk\"ahler manifolds and flag varieties. We pay special attention to the cases where this leads to a Jordan algebra structure or a graded Frobenius algebra.Comment: AMSTeX v2.1, 46 page

Monodromy of Cyclic Coverings of the Projective Line

We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree.Comment: 47 pages (to appear in Inventiones Mathematicae

Allelic losses in carcinoma in situ and testicular germ cell tumours of adolescents and adults: evidence suggestive of the linear progression model

Testicular germ cell tumours (TGCTs) may arise through a process of multi-step carcinogenesis, and loss of heterozygosity (LOH) at specific loci is likely to be an important early event, although this has not been studied in detail. In order to explore the pathogenetic relationships among TGCTs, we investigated the genetic changes in testicular tumours that exhibit a disease continuum through the precursor carcinoma in situ (CIS) to either seminoma (SE) and/or non-seminomatous germ cell tumour (NSGCT). Universal amplification has been performed on 87 TGCT specimens and 36 samples of CIS cells microdissected from single paraffin-embedded tumour sections from 40 patients, including multiple specimens of CIS and TGCT cells of varied histology microdissected from 24 individual patients. Seventy-seven microsatellite markers were used to assay these samples for LOH at candidate regions selected from the literature, mapping to 3q, 5q, 9p, 11p, 11q, 12q, 17p and 18q. Construction of deletion maps for each of these regions identified common sites of deletion at 3q27–q28, 5q31, 5q34–q35, 9p22–p21 and 12q22, which correlate with allelic losses we have also observed in the precursor CIS cells. Evidence for allelic loss at 3q27–q28 was observed in all of the embryonal carcinoma samples analysed. We conclude that inactivation of gene(s) within these regions are likely to be early events in the development and progression of TGCTs. These results also provide molecular evidence in support of the hypothesis that SE is an intermediate stage of development within a single neoplastic pathway of progression from CIS precursor cells to NSGCT. © 2000 Cancer Research Campaig

The structure of 2D semi-simple field theories

I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the Gromov-Witten potential is described by Givental's Fock space formulae. This leads to the reconstruction of Gromov-Witten invariants from the quantum cup-product at a single semi-simple point and from the first Chern class, confirming Givental's higher-genus reconstruction conjecture. The proof uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio

N- and KRAS mutations in primary testicular germ cell tumors: Incidence and possible biological implications

Recently, conflicting results have been reported on the incidence of RAS mutations in primary testicular germ cell tumors of adults (TGCTs). In four studies a low incidence of mutations (less than 15%) in a variety of TGCTs or derived cell lines was found, whereas in two other studies a high incidence of N- or KRAS mutations (over 40%) was shown. A total of 62 testicular seminomas (SE) and 34 nonseminomatous TGCTs (NS) were studied thus far. The largest series consisted of 42 TGCTs, studied on paraffin embedded tissue. We present the results of analysis for the presence of N- and KRAS mutations, in codons 12, 13, and 61, in snap frozen samples of 100 primary TGCTs, comprising 40 SE and 60 NS. Using the polymerase chain reaction (PCR) and allele specific oligonucleotide hybridization (ASO), mutations were found in five SE (three in NRAS and two in KRAS, all codon 12), and in one NS (KRAS, codon 12). To exclude underestimation of the incidence of RAS mutations in TGCTs due to the presence of an excess of wild type alleles in the analyzed sample, a PCR technique preferentially ampli

Constraining the Kahler Moduli in the Heterotic Standard Model

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles, constrain the set of Kaehler moduli which give rise to realistic compactifications of the strongly coupled heterotic string. When vector bundles are constructed using extensions, we provide simple rules to determine lower and upper bounds to the region of the Kaehler moduli space where such compactifications can exist. We show how small these regions can be, working out in full detail the case of the recently proposed Heterotic Standard Model. More explicitely, we exhibit Kaehler classes in these regions for which the visible vector bundle is stable. On the other hand, there is no polarization for which the hidden bundle is stable.Comment: 28 pages, harvmac. Exposition improved, references and one figure added, minor correction