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of 33
pro vyhledávání: '"Kalm, Håkan Samuelsson"'
Given a reduced analytic space $Y$ we introduce a class of {\it nice} cycles, including all effective $\mathbb{Q}$-Cartier divisors. Equidimensional nice cycles that intersect properly allow for a natural intersection product. Using $\bar{\partial}$-
Externí odkaz:
http://arxiv.org/abs/2112.11247
Autor:
Kalm, Håkan Samuelsson
For any holomorphic mapping $f\colon X\to Y$ between a complex manifold $X$ and a complex Hermitian manifold $Y$ we extend the pullback $f^*$ from smooth forms to a class of currents. We provide a basic calculus for this pullback and show under quite
Externí odkaz:
http://arxiv.org/abs/2004.08165
Given pure-dimensional (generalized) cycles $\mu_1$ and $\mu_2$ on a complex manifold $Y$ we introduce a product $\mu_1\diamond_{Y} \mu_2$ that is a generalized cycle whose multiplicities at each point are the local intersection numbers at the point.
Externí odkaz:
http://arxiv.org/abs/2003.06180
We prove that any smooth mapping between reduced analytic spaces induces a natural pullback operation on smooth differential forms.
Externí odkaz:
http://arxiv.org/abs/2003.01959
On any pure $n$-dimensional, possibly non-reduced, analytic space $X$ we introduce the sheaves $\mathscr{E}_X^{p,q}$ of smooth $(p,q)$-forms and certain extensions $\mathscr{A}_X^{p,q}$ of them such that the corresponding Dolbeault complex is exact,
Externí odkaz:
http://arxiv.org/abs/2002.01797
In this article we develop intersection theory in terms of the $\mathcal{B}$-group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct images of Chern
Externí odkaz:
http://arxiv.org/abs/1908.11759
On a reduced analytic space $X$ we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient $
Externí odkaz:
http://arxiv.org/abs/1812.03054
Autor:
Andersson, Mats, Lärkäng, Richard, Ruppenthal, Jean, Kalm, Håkan Samuelsson, Wulcan, Elizabeth
Publikováno v:
J. Geom. Anal. 30 (2020), no. 3, 2974-3001
We study the solvability in $L^p$ of the $\bar\partial$-equation in a neighborhood of a canonical singularity on a complex surface, a so-called du Val singularity. We get a quite complete picture in case $p=2$ for two natural closed extensions $\bar\
Externí odkaz:
http://arxiv.org/abs/1804.01004
Autor:
Kalm, Håkan Samuelsson, Sera, Martin
Publikováno v:
Mathematica Scandinavica 126, no. 2 (May 2020), 221-228
For a reduced pure dimensional complex space $X$, we show that if Barlet's recently introduced sheaf $\alpha_X^1$ of holomorphic $1$-forms or the sheaf of germs of weakly holomorphic $1$-forms is locally free, then $X$ is smooth. Moreover, we discuss
Externí odkaz:
http://arxiv.org/abs/1709.09833
Autor:
Kalm, Håkan Samuelsson
We make the classical Dickenstein-Sessa canonical representation in local moderate cohomology explicit by an integral formula. We also provide a similar representation of the higher local moderate cohomology groups. The results are related to holomor
Externí odkaz:
http://arxiv.org/abs/1703.03661