Search results for "Algebraic Geometry"
showing 10 items of 356 documents
p-Brauer characters ofq-defect 0
1994
For ap-solvable groupG the number of irreducible Brauer characters ofG with a given vertexP is equal to the number of irreducible Brauer characters of the normalizer ofP with vertexP. In this paper we prove in addition that for solvable groups one can control the number of those characters whose degrees are divisible by the largest possibleq-power dividing the order of |G|.
A note on coverings with special fibres and monodromy group $ S_{d}$
2012
We consider branched coverings of degree over with monodromy group , points of simple branching, special points and fixed branching data at the special points, where is a smooth connected complex projective curve of genus , and , are integers with . We prove that the corresponding Hurwitz spaces are irreducible if .
Der Satz von Tits für PGL2(R), R ein kommutativer Ring vom stabilen Rang 2
1996
Certain permutation groups on sets with distance relation are characterized as groups of projectivities PGL2(R) on the projective line over a commutative ring R of stable rank 2, thus generalizing a classical result of Tits where R is a field.
On the divisor class group of double solids
1999
For a double solid V→ℙ3> branched over a surface B⊂ℙ3(ℂ) with only ordinary nodes as singularities, we give a set of generators of the divisor class group \(\) in terms of contact surfaces of B with only superisolated singularities in the nodes of B. As an application we give a condition when H* (˜V , ℤ) has no 2-torsion. All possible cases are listed if B is a quartic. Furthermore we give a new lower bound for the dimension of the code of B.
Computation of the topological type of a real Riemann surface
2012
We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$, namely, the number of its connected components, and whether this set divides the surface into one or two connected components. This is achieved by transforming an arbitrary canonical homology basis to a homology basis where the $\mathcal{A}$-cycles are invariant under the anti-holomorphic involution $\tau$.
The geometry of surfaces in 4-space from a contact viewpoint
1995
We study the geometry of the surfaces embedded in ℝ4 through their generic contacts with hyperplanes. The inflection points on them are shown to be the umbilic points of their families of height functions. As a consequence we prove that any generic convexly embedded 2-sphere in ℝ4 has inflection points.
Mirror symmetry and toric degenerations of partial flag manifolds
1998
In this paper we propose and discuss a mirror construction for complete intersections in partial flag manifolds $F(n_1, ..., n_l, n)$. This construction includes our previous mirror construction for complete intersection in Grassmannians and the mirror construction of Givental for complete flag manifolds. The key idea of our construction is a degeneration of $F(n_1, ..., n_l, n)$ to a certain Gorenstein toric Fano variety $P(n_1, ..., n_l, n)$ which has been investigated by Gonciulea and Lakshmibai. We describe a natural small crepant desingularization of $P(n_1, ..., n_l, n)$ and prove a generalized version of a conjecture of Gonciulea and Lakshmibai on the singular locus of $P(n_1, ..., n…
Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects
2016
We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic eightfold $Z$, described by the four authors, is isomorphic to an irreducible component of a moduli space of Gieseker stable torsion sheaves or rank three torsion free sheaves. For a very general such cubic fourfold, we show that $Z$ is isomorphic to a connected component of a moduli space of tilt-stable objects in the derived category and to a moduli space of Bridgeland stable objects in the Kuznetsov component. Moreover, the contraction between $Z'$ and $Z$ i…
Convexly generic curves in R 3
1988
We study curves immersed in R 3, with special interest in the description of their convex hull frontier structure from a global viewpoint. Genericity conditions are set for these curves by looking at the singularities of height functions on them. We define panel structures for convexly generic curves and work out numerical relations involving the number of tritangent support planes. As a consequence, a generic version of the 4-vertex theorem for convex curves in R 3 is obtained.
Elementary Integration of Superelliptic Integrals
2021
Consider a superelliptic integral $I=\int P/(Q S^{1/k}) dx$ with $\mathbb{K}=\mathbb{Q}(\xi)$, $\xi$ a primitive $k$th root of unity, $P,Q,S\in\mathbb{K}[x]$ and $S$ has simple roots and degree coprime with $k$. Note $d$ the maximum of the degree of $P,Q,S$, $h$ the logarithmic height of the coefficients and $g$ the genus of $y^k-S(x)$. We present an algorithm which solves the elementary integration problem of $I$ generically in $O((kd)^{\omega+2g+1} h^{g+1})$ operations.