A pullback operation on a class of currents

For any holomorphic map $f\colon X\to Y$ between a complex manifold $X$ and a complex Hermitian manifold $Y$ we extend the pullback $f^*$ from smooth forms to a class of currents in a cohomologically sound way. We provide a basic calculus for this pullback. The class of currents we consider contains in particular the Lelong current of any analytic cycle. Our pullback depends in general on the Hermitian structure of $Y$ but coincides with the usual pullback of currents in case $f$ is a submersion. The construction is based on the Gysin mapping in algebraic geometry.Comment: Theorem 1.2 is improve

Presence or absence of analytic structure in maximal ideal spaces

We study extensions of Wermer's maximality theorem to several complex variables. We exhibit various smoothly embedded manifolds in complex Euclidean space whose hulls are non-trivial but contain no analytic disks. We answer a question posed by Lee Stout concerning the existence of analytic structure for a uniform algebra whose maximal ideal space is a manifold.Comment: Comments are welcome

One parameter regularizations of products of residue currents

We show that Coleff-Herrera type products of residue currents can be defined by analytic continuation of natural functions depending on one complex variable.Comment: 8 page

Segre numbers, a generalized King formula, and local intersections

Let $\mathcal J$ be an ideal sheaf on a reduced analytic space $X$ with zero set $Z$. We show that the Lelong numbers of the restrictions to $Z$ of certain generalized Monge-Amp\`ere products $(dd^c\log|f|^2)^k$, where $f$ is a tuple of generators of $\mathcal J$, coincide with the so-called Segre numbers of $\mathcal J$, introduced independently by Tworzewski and Gaffney-Gassler. More generally we show that these currents satisfy a generalization of the classical King formula that takes into account fixed and moving components of Vogel cycles associated with $\mathcal J$. A basic tool is a new calculus for products of positive currents of Bochner-Martinelli type. We also discuss connections to intersection theory

Dissertatio de incrementis frigoris, in terris borealibus annis proxime praeterlapsis observatis, quam cons. ampl. fac. phil. Aboëns. praeside d:no Petro Kalm, s.s. theol. doct. oecon. profess. reg. & ordin. design. equite de ord. Reg. Was. Reg. Acad. Scient. Stockh. & Societ. Lit. Upsal. membro, pro summis in philosophia honoribus publice ventilandam sistit Isaacus Nordlund, Borea-Fenno. In auditorio majori die XV. Julii anni MDCCLXXII. horis ante meridiem solitis

Painovuosi nimekkeestä.Invocatio: D.D.Arkit: A4 B2

Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L2-cohomology classes

In the present paper, we derive an adjunction formula for the Grauert-Riemenschneider canonical sheaf of a singular hypersurface V in a complex manifold M. This adjunction formula is used to study the problem of extending L2-cohomology classes of dbar-closed forms from the singular hypersurface V to the manifold M in the spirit of the Ohsawa-Takegoshi-Manivel extension theorem. We do that by showing that our formulation of the L2-extension problem is invariant under bimeromorphic modifications, so that we can reduce the problem to the smooth case by use of an embedded resolution of V in M. The smooth case has recently been studied by Berndtsson.Comment: 20 page

Enfaldiga tankar om nyttan som England kan hafwa af sina nybyggen i norra America, med philosophiska facult. tilstånd under oeconomiae profess. och Kongl. Svenska Vetenskaps Academies samt Ups. Vet. Soc. ledamots herr Pehr Kalms inseende, til allmän granskning för lager-kransen framstälte af Sven Gowinius. Nylänninge. Uti academiens nedre läro-sal, f. m. den 20 Junii 1763

Inv: Med Guds Hjelp.Painovuosi nimekkeestä.Arkit: A-B4 C3

Muudatused arstiteaduskonnas Tartu Ülikooli struktuurireformi käigus

Eesti Arst 2016; 95(1):10–1