Representability of Chern-Weil forms

In this paper we look at two naturally occurring situations where the following question arises. When one can find a metric so that a Chern-Weil form can be represented by a given form ? The first setting is semi-stable Hartshorne-ample vector bundles on complex surfaces where we provide evidence for a conjecture of Griffiths by producing metrics whose Chern forms are positive. The second scenario deals with a particular rank-2 bundle (related to the vortex equations) over a product of a Riemann surface and the sphere.Comment: Final version. To appear in Mathematische Zeitschrif

Bargmann-Fock extension from Singular Hypersurfaces

We establish sufficient conditions for extension of weighted square integrable holomorphic functions from a possibly singular hypersurface to the ambient affine space. The norms we use are the so-called Bargmann-Fock norms, and thus there are restrictions on the singularities and the density of the hypersurface. Our sufficient conditions are that it has density less than 1, and is uniformly flat in a sense that extends to singular varieties the notion of uniform flatness introduced earlier. We present an example of Ohsawa showing that uniform flatness is not necessary for extension in the singular case, and find an example showing that, for rather different reasons, it is also not necessary for the smooth case. The latter answers in the negative a question posed in an earlier paper of the second author.Comment: Corrected the email address of the second author. To appear in Crelle's Journa

A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds

A vector bundle E on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. A theorem of Nori implies that E is finite if and only if the pullback of E to some finite etale Galois covering of X is trivial. We prove the same statement when X is a compact complex manifold admitting a Gauduchon astheno-Kahler metric

The deformed Hermitian Yang-Mills equation on three-folds

We prove an existence result for the deformed Hermitian Yang-Mills equation for the full admissible range of the phase parameter, i.e., $\hat{\theta} \in (\frac{\pi}{2},\frac{3\pi}{2})$, on compact complex three-folds conditioned on a necessary subsolution condition. Our proof hinges on a delicate analysis of a new continuity path obtained by rewriting the equation as a generalised Monge-Amp\`ere equation with mixed sign coefficients.Comment: Corrected some reference

Ursula Pritham, interviewed by Hillary Jackson, Part 2

Ursula Pritham, interviewed by Hillary Jackson, November 5, 2001. Pritham, who was born in New York City in 1955, talks about her background (Swiss); serving in the Army Nurse Core; serving stateside, in Germany, and in Korea; initial training; Vietnam; Gulf War; husband; typical day; toll on family; public support; funny moments; husband’s experiences in the military; his views of the military; travel; male/female relationships in the military; relationships among the women; harassment; her thoughts about the military. Text: 24 pp. transcript. Time: 01:30:05. Listen: Part 1: mfc_na3238_c2345_01 Part 2: mfc_na3238_c2346_01 Part 3: mfc_na3238_c2346_02https://digitalcommons.library.umaine.edu/mf144/1059/thumbnail.jp

Ursula Pritham, interviewed by Hillary Jackson, Part 3

Ursula Pritham, interviewed by Hillary Jackson, November 5, 2001. Pritham, who was born in New York City in 1955, talks about her background (Swiss); serving in the Army Nurse Core; serving stateside, in Germany, and in Korea; initial training; Vietnam; Gulf War; husband; typical day; toll on family; public support; funny moments; husband’s experiences in the military; his views of the military; travel; male/female relationships in the military; relationships among the women; harassment; her thoughts about the military. Text: 24 pp. transcript. Time: 01:30:05. Listen: Part 1: mfc_na3238_c2345_01 Part 2: mfc_na3238_c2346_01 Part 3: mfc_na3238_c2346_02https://digitalcommons.library.umaine.edu/mf144/1060/thumbnail.jp