Browsing 1 - Oberwolfach Preprints (OWP) by MSC "14"
Now showing items 21-40 of 48
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The Magic Square of Reflections and Rotations
[OWP-2018-13] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-01)We show how Coxeter’s work implies a bijection between complex reflection groups of rank two and real reflection groups in 0(3). We also consider this magic square of reflections and rotations in the framework of Clifford ... -
A McKay Correspondence for Reflection Groups
[OWP-2018-14] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-02)We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies ... -
The Minimal Resolution Conjecture on a general quartic surface in $\mathbb P^3$
[OWP-2017-21] (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-27)Mustaţă has given a conjecture for the graded Betti numbers in the minimal free resolution of the ideal of a general set of points on an irreducible projective algebraic variety. For surfaces in $\mathbb P^3$ this conjecture ... -
Monoid valuations and value ordered supervaluations
[OWP-2011-17] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations ... -
New representations of matroids and generalizations
[OWP-2011-18] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This ... -
Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into a projective variety intersecting hypersurfaces
[OWP-2010-19] (Mathematisches Forschungsinstitut Oberwolfach, 2010)In 1985, Fujimoto established a non-integrated defect relation for meromorphic maps of complete Kähler manifolds into the complex projective space intersecting hyperplanes in general position. In this paper, we generalize ... -
Numerical Invariants and Moduli Spaces for Line Arrangements
[OWP-2017-02] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-01)Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane ... -
On a Group Functor Describing Invariants of Algebraic Surfaces
[OWP-2019-08] (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-01)Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of ... -
On the Complement of the Richardson Orbit
[OWP-2010-09] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-13)We consider parabolic subgroups of a general algebraic group over an algebraically closed field $k$ whose Levi part has exactly $t$ factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup $P$ ... -
On the Derived Category of Grassmannians in Arbitrary Characteristic
[OWP-2013-24] (Mathematisches Forschungsinstitut Oberwolfach, 2013-12-09)In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's well-known characteristic-zero results we construct dual exceptional collections on them (which are however not strong) as well ... -
On the Directionally Newton-non-degenerate Singularities of Complex Hypersurfaces
[OWP-2008-16] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We introduce a minimal generalization of Newton-non-degenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newton-non-degenerate if the local embedded ... -
On the Gauss Algebra of Toric Algebras
[OWP-2018-07] (Mathematisches Forschungsinstitut Oberwolfach, 2018-04-25)Let $A$ be a $K$-subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\mathbb{G}(A)$ of $A$ is generated by monomials of ... -
On the geometry of regular maps from a quasi-projective surface to a curve
[OWP-2013-03] (Mathematisches Forschungsinstitut Oberwolfach, 2013-03-14)We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X. -
On the non-analyticity locus of an arc-analytic function
[OWP-2009-03] (Mathematisches Forschungsinstitut Oberwolfach, 2009-02-21)A function is called arc-analytic if it is real analytic on each real analytic arc. In real analytic geometry there are many examples of arc-analytic functions that are not real analytic. Arc analytic functions appear ... -
On the δ=const Collisions of Singularities of Complex Plane Curves
[OWP-2008-15] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or ... -
Products of pairs of Dehn twists and maximal real Lefschetz fibrations
[OWP-2011-32] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic ... -
Real Analyticity is Concentrated in Dimension 2
[OWP-2018-23] (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-05)We prove that a real-valued function on a real analytic manifold is analytic whenever all its restrictions to $2$-dimensional analytic submanifolds are analytic functions. We also obtain analogous results in the framework ... -
Real Enumerative Invariants Relative to the Anti-Canonical Divisor and their Refinement
[OWP-2023-02] (Mathematisches Forschungsinstitut Oberwolfach, 2023-03-24)We introduce new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from the appropriate enumeration of real elliptic curves. These invariants admit a refinement (according to ... -
Real group orbits on flag ind-varieties of SL (∞, C)
[OWP-2016-01] (Mathematisches Forschungsinstitut Oberwolfach, 2016-05-10)We consider the complex ind-group $G=SL (\infty, \mathbb{C})$ and its real forms $G^0=SU(\infty,\infty)$, $SU(p,\infty)$, $SL(\infty,\mathbb{R})$, $SL(\infty,\mathbb{H})$. Our main object of study are the $G^0$-orbits on ... -
Simple vector bundles on plane degenerations of an elliptic curve
[OWP-2009-20] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-13)In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main ...