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| | | Vortrag wegen Island-Vulkanausbruch abgesagt!
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| 19.04.10, | 16:15 | Gregory G. Smith
(Ontario) |
| | | Old and new perspectives on Hilbert functions
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| | Abstract
Hilbert functions are fundamental invariants in algebra geometry
and commutative algebra. After recalling the basic definitions
and motivating examples, we will discuss Macaulay's characterization
for the collection of all Hilbert functions. We'll then contrast
this with a newer viewpoint and look at potential applications.
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| 26.04.10, | 16:15 | Bernd Martin (Cottbus) |
| | | "Massey-Produkte"
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| 03.05.10, | 16:15 | Jarek Wisniewski (Warschau) |
| | | Fano spaces and marked polytopes
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| | Abstract This will be a "work in progress" report on a joint project with Klaus Altmann. I will try to explain the geometry of (some) blow ups of projective spaces (and their small modifications) from the
point of view of their cones of movable divisors (and their duals).
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| 10.05.10, | 16:15 | Vortrag fällt aus! |
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| 17.05.10, | 16:15 | Kein Seminar: Sonderseminartag am 19. Mai 2010! |
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| 19.05.10, | 9:15 | Orsola Tommasi (Hannover) |
| | | Diskriminantenvarietäten und der Modulraum ebener Kurven vom Grad 4 mit einer ausgezeichneten Bitangenten.
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| 11:15 | Jimmy Dillies (Utah, USA) |
| | | 'Calabi-Yau varieties and K3 symmetries'
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| 14:15 | Elena Martinengo (Rom) |
| | | An overview on deformation theory: from classical techniques to
infinity-groupoids.
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| | Abstract:
We will briefly recall basic tools in deformation theory via
differential graded Lie algebras and show how this language allows for
an immediate proof of Kodaira's principle on obstructions to
deformations of complex manifolds. As further examples, we will
present new results on obstructions to deformations of Hitchin pairs
and on the local structure of the moduli space of locally free shaves
on a given manifold.
In the second part of the talk, we will reinterpret the
Kodaira-Spencer approach to deformations of complex manifolds through
the modern language of stacks, we will review recent results in this
direction and show how this leads to infinity-groupoids as the natural
and suitable language for the "local to global" approach to
deformations.As illustrative examples of this, we will describe deformations of
coherent sheaves and of singular varieties.
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| 16:15 | Masoud Kamgarpour (Britisch Columbia, Canada) |
| | | "Stacky abelianization of algebraic groups"
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| 24.05.10, | 16:15 | Pfingsten! |
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| 24.05.10, | 16:15 | Marianne Merz (FU-Berlin) |
| | | Perverse Garben
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| | Abstract: Perverse Garben haben ihren Ursprung in der Schnitthomologie. Ich beginne daher mit einer topologischen
Einführung nach Goresky/MacPherson und nach der Definition perverser Garben als t-Struktur auf der
derivierten Kategorie, möchte ich noch auf die wichtigsten Theoreme eingehen.
Es gibt noch eine nette Anwendung, die Kalai Vermutung: g(P)>=g(F)g(P/F).
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| 07.06.10, | 16:15 | Ursula Ludwig (Berlin / Freiburg) |
| | | Stratifizierte Morse-Theorie und perverse Garben
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| | Abstract:In the nice book 'Stratified Morse Theory' (1982) Goresky and MacPherson developed a Morse theory for stratified Morse functions $f: X \ra \RRR$ on a (Whitney) stratified space $X$. Their goal was to understand better some properties of the intersection homology, a new invariant for stratified spaces they had introduced a couple of years before.
In the complex case the situation is particularly nice: One gets stratified Morse inequalities relating the number of critical points of the Morse function to the intersection homology of the space. The singular points of $X$ contribute to this Morse inequalities in middle degree only and have to be counted with multiplicities. This contribution can be explained in a geometric way, but also in the more abstract language of perverse sheaves, namely in terms of the 'nearby' and 'vanishing cycles'.
In this talk I will try to present the above results, which however are not directly related to my own research.
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| 14.06.10, | 16:15 | NoGAGS am 17. & 18. Juni 2010 |
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| 21.06.10, | 16:15 | Sandra Di Rocco (Stockholm) |
| | | Positivity for Toric bundles
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| | Abstract: I will review existing results on positivity criteria for equivariant vector bundles on toric varieties and report
on some conjectures and preliminary results in progress obtained with G. Smith and K. Jabbusch.
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| 28.06.10, | 16:15 | Klaus Haberland (Jena) |
| | | Zur Arithmetik einiger K3-Flächen
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| 05.07.10, | 16:15 | Dmitriy Pochekutov (TU-Cottbus) |
| | | On diagonals of the Laurent series of rational functions
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| | Abstract: The diagonals of power series in several variables
arise naturally in the problems of the algebraicity
and $D$-finiteness of the sums of power series.
We give sufficient conditions for the algebraicity
of diagonals basing on the theory of multidimensional
residues and topological properties of the complements
to collections of complex hypersurfaces in complex
analytic varieties.
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| 12.07.10, | 14:15 | Maria Angelica Cueto (Berkeley) |
| | | Tropical secant graphs of monomial curves
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| | Abstract: The first secant variety of a monomial curve is a threefold with an action
by a one-dimensional torus. Its tropicalization is a three-dimensional fan
with one-dimensional lineality space, so the tropical threefold is
represented by a balanced graph. Our main result is an explicit
construction of that graph.
As a consequence we obtain algorithms to effectively compute the multidegree
and Chow polytope of an arbitrary monomial curve. This generalizes an
earlier degree formula due to Ranestad. The combinatorics underlying our
construction is rather delicate, and it is based on a refinement of the
theory of geometric tropicalization due to Hacking, Keel and Tevelev.
The key step in the construction of the balanced graph involves
finding a suitable compactification (a ``tropical compactification'')
of the complement of a binomial arrangement in the 2-torus
$(\mathbb{C}^*)^2$, whose boundary divisor has no three components
intersecting at a point. Such compactification can be obtained by
resolving all multiple intersections in $\mathbb{P}^2$ by blowups, and
realizes the wonderful compactification of De Concini and Procesi.
This is joint work with Shaowei Lin (Eprint: arXiv:1005.3364v1).
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| 12.07.10, | 16:15 | Victor Batyrev (Tübingen) |
| | | A generalization of a theorem of White
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| | Abstract: This is a joint work with Johannes Hofscheier.
An n-dimensional simplex \Delta in \R^n is called empty lattice simplex if
\Delta \cap\Z^n is exactly the set of vertices of \Delta . A theorem of G.
K. White shows that if n=3 then any empty lattice simplex \Delta
\subset\R^3 is isomorphic up to an unimodular affine linear transformation
to a lattice tetrahedron whose all vertices have third coordinate 0 or 1.
We prove a generalization of this theorem for an arbitrary odd dimension
n=2d-1 which in some form was conjectured by Seb\H{o} and Borisov. This
result implies a classification of all 2d-dimensional isolated Gorenstein
cyclic quotient singularities with minimal log-discrepancy at least d
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| 19.07.10, | 16:15 | Ivan V. Arzhantsev (Moskau/ Tübingen) |
| | | Equivariant compactifications of commutative unipotent groups
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| | Abstract: The study of equivariant compactifications of a commutative unipotent
group G may be regarded as an additive analogue
of toric geometry. B.Hassett and Yu.Tschinkel (Int. Math. Res. Notices
20 (1999), 1211-1230) introduced a remarkable
correspondence between generically transitive G-actions and
finite-dimensional local algebras. We develop
Hassett-Tschinkel's correspondence and calculate modality of generically
transitive G-actions on projective spaces,
classify actions of modality one and characterize generically transitive
G-actions on projective hypersurfaces
of given degree. In particular, G-actions on projective quadrics are
studied. This part of the talk is based on
a joint work with Elena Sharoyko. In the second part we classify flag
varieties which may be realized as
equivariant compactifications of G.
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| 19.07.10, | 16:15 | Fedor Bogomolov (New York / Moskau) |
| | | Closed holomorphic differentials and holomorphic webs
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| | Abstract: I will report on progress in our joint work
with Bruno de Oliveira.
We call a symmetric holomorphic differential $s$ on a complex manifold closed
if it can be written as $\prod df_i^{n_i}$ in the local
neighborhood of some point $x_o$ of the manifold.
This property holds then for a complementary of a finite set of divisors
and hence such a differential defines a holomorphic web--a set of local
codimension one foliations on the manifold ( possibly singular).
Note that any symmetric differential on surface defines a similar
web. However the webs defined by closed differentials are very special
and provide with restrictions on the topology of the ambient surface
( or manifold). I will discuss some results and conjectures.
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