| 1. |
- Andersson, Mats, 1957, et al.
(författare)
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One parameter regularizations of products of residue currents
- 2017
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Ingår i: Trends in Mathematics. - Cham : Springer. - 2297-0215 .- 2297-024X. - 9783319524719 ; , s. 81-90
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Bokkapitel (refereegranskat)abstract
- © 2017 Springer International Publishing. We show that Coleff–Herrera type products of residue currents can be defined by analytic continuation of natural functions depending on one complex variable.
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| 2. |
- Andersson, Mats, 1957, et al.
(författare)
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Segre numbers, a generalized King formula, and local intersections
- 2017
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Ingår i: Journal für die Reine und Angewandte Mathematik. - : Walter de Gruyter GmbH. - 1435-5345 .- 0075-4102. ; 728:728, s. 105-136
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Tidskriftsartikel (refereegranskat)abstract
- 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–Ampère products $(dd^c \log |f|^2)^k$, where $f$ is a tuple of generators of $\mathcal{J}$, coincide with theso-called Segre numbers of $\mathcal{J}$, introduced independently by Tworzewski, Achilles–Manaresi,and Gaffney–Gassler. More generally we show that these currents satisfy a generalization ofthe classical King formula that takes into account fixed and moving components of Vogelcycles associated with $\mathcal{J}$. A basic tool is a new calculus for products of positive currents ofBochner–Martinelli type. We also discuss connections to intersection theory.
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| 3. |
- Izzo, Alexander, et al.
(författare)
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Presence or absence of analytic structure in maximal ideal spaces
- 2016
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 366:1-2, s. 459-478
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Johansson, Petter, et al.
(författare)
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A Ronkin type function for coamoebas
- 2017
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Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1050-6926 .- 1559-002X. ; 27:1, s. 643-670
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Tidskriftsartikel (refereegranskat)abstract
- The Ronkin function plays a fundamental role in the theory of amoebas. We introduce an analogue of the Ronkin function in the setting of coamoebas. It turns out to be closely related to a certain toric arrangement known as the shell of the coamoeba and we use our Ronkin type function to obtain some properties of it.
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| 5. |
- Ruppenthal, Jean, et al.
(författare)
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Adjunction for the Grauert-Riemenschneider canonical sheaf and extension of L²-cohomology classes
- 2015
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Ingår i: Indiana University Mathematics Journal. - : Indiana University Mathematics Journal. - 0022-2518. ; 64:2, s. 533-558
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Tidskriftsartikel (refereegranskat)abstract
- 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 $L^2$-cohomology classes of $\bar{\partial}$-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 $L^2$-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.
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| 6. |
- Ruppenthal, Jean, et al.
(författare)
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Explicit Serre duality on complex spaces
- 2017
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 1090-2082 .- 0001-8708. ; 305, s. 1320-1355
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we use recently developed calculus of residue currentstogether with integral formulas to give a new explicit analytic realization, as wellas a new analytic proof of Serre duality on any reduced pure n-dimensional paracompact complex space X. At the core of the paper is the introduction of concretefine sheaves $A^{n,q}_X$ of certain currents on X of bidegree (n,q), such that the corresponding Dolbeault complex becomes, in a certain sense, a dualizing complex. Inparticular, if X is Cohen-Macaulay (e.g., Gorenstein or a complete intersection)then this Dolbeault complex becomes an explicit fine resolution of the Grothendieck dualizing sheaf.
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| 7. |
- Samuelsson Kalm, Håkan, 1976
(författare)
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Holomorphic forms, the $\bar{\partial}$-equation, and duality on a reduced complex space
- 2015
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Ingår i: arXiv math.
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- We study two natural notions of holomorphic forms on a reduced pure $n$-dimensional complex space $X$: sections of the sheaves $\Omega_X^{\bullet}$ of germs of holomorphic forms on $X_{reg}$ that have a holomorphic extension to some ambient complex manifold, and sections of the sheaves $\omega_X^{\bullet}$ introduced by Barlet. We show that $\Omega_X^p$ and $\omega_X^{n-p}$ are Serre dual to each other in a certain sense. We also provide explicit, intrinsic and semi-global Koppelman formulas for the $\bar{\partial}$-equation on $X$ and introduce fine sheaves $\mathscr{A}_X^{p,q}$ and $\mathscr{B}_X^{p,q}$ of $(p,q)$-currents on $X$, that are smooth on $X_{reg}$, such that $(\mathscr{A}_X^{p,\bullet},\bar{\partial})$ is a resolution of $\Om_X^p$ and, if $\Omega_X^{n-p}$ is Cohen-Macaulay, $(\mathscr{B}_X^{p,\bullet},\bar{\partial})$ is a resolution of $\omega_X^{p}$.
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