812 research outputs found
Quantum symmetries and exceptional collections
We study the interplay between discrete quantum symmetries at certain points
in the moduli space of Calabi-Yau compactifications, and the associated
identities that the geometric realization of D-brane monodromies must satisfy.
We show that in a wide class of examples, both local and compact, the monodromy
identities in question always follow from a single mathematical statement. One
of the simplest examples is the Z_5 symmetry at the Gepner point of the
quintic, and the associated D-brane monodromy identity
Three embeddings of the Klein simple group into the Cremona group of rank three
We study the action of the Klein simple group G consisting of 168 elements on
two rational threefolds: the three-dimensional projective space and a smooth
Fano threefold X of anticanonical degree 22 and index 1. We show that the
Cremona group of rank three has at least three non-conjugate subgroups
isomorphic to G. As a by-product, we prove that X admits a Kahler-Einstein
metric, and we construct a smooth polarized K3 surface of degree 22 with an
action of the group G.Comment: 43 page
A characterization of compact complex tori via automorphism groups
We show that a compact Kaehler manifold X is a complex torus if both the
continuous part and discrete part of some automorphism group G of X are
infinite groups, unless X is bimeromorphic to a non-trivial G-equivariant
fibration. Some applications to dynamics are given.Comment: title changed, to appear in Math. An
A travel guide to the canonical bundle formula
We survey known results on the canonical bundle formula and its applications
in algebraic geometry.Comment: 17 pages, to appear in the Proceedings of the conference Birational
Geometry and Moduli Space
Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type
Let X be a compact Kahler holomorphic-symplectic manifold, which is
deformation equivalent to the Hilbert scheme of length n subschemes of a K3
surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L)
vanishes and c_1(L) is primitive. Assume that the two dimensional subspace
H^{2,0}(X) + H^{0,2}(X), of the second cohomology of X with complex
coefficients, intersects trivially the integral cohomology. We prove that the
linear system of L is base point free and it induces a Lagrangian fibration on
X. In particular, the line-bundle L is effective. A determination of the
semi-group of effective divisor classes on X follows, when X is projective. For
a generic such pair (X,L), not necessarily projective, we show that X is
bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion
sheaves, each with pure one dimensional support, on a projective K3 surface.Comment: 34 pages. v3: Reference [Mat5] and Remark 1.8 added. Incorporated
improvement to the exposition and corrected typos according to the referees
suggestions. To appear in the proceedings of the conference Algebraic and
Complex Geometry, Hannover 201
Homological Type of Geometric Transitions
The present paper gives an account and quantifies the change in topology
induced by small and type II geometric transitions, by introducing the notion
of the \emph{homological type} of a geometric transition. The obtained results
agree with, and go further than, most results and estimates, given to date by
several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark
3.2 were added. This is the final version accepted for publication in the
journal Geometriae Dedicat
Disorder Effect on the Vortex Pinning by the Cooling Process Control in the Organic Superconductor -(BEDT-TTF)Cu[N(CN)]Br
We investigate the influence of disorders in terminal ethylene groups of
BEDT-TTF molecules (ethylene-disorders) on the vortex pinning of the organic
superconductor -(BEDT-TTF)Cu[N(CN)]Br. Magnetization
measurements are performed under different cooling-processes. The second peak
in the magnetization hysteresis curve is observed for all samples studied, and
the hysteresis width of the magnetization becomes narrower by cooling faster.
In contradiction to the simple pinning effect of disorder, this result shows
the suppression of the vortex pinning force by introducing more
ethylene-disorders. The ethylene-disorder domain model is proposed for
explaining the observed result. In the case of the system containing a moderate
number of the ethylene-disorders, the disordered molecules form a domain
structure and it works as an effective pinning site. On the contrary, an excess
number of the ethylene-disorders may weaken the effect of the domain structure,
which results in the less effective pinning force on the vortices.Comment: 6 pages, 6 figure
Moduli of Abelian varieties, Vinberg theta-groups, and free resolutions
We present a systematic approach to studying the geometric aspects of Vinberg
theta-representations. The main idea is to use the Borel-Weil construction for
representations of reductive groups as sections of homogeneous bundles on
homogeneous spaces, and then to study degeneracy loci of these vector bundles.
Our main technical tool is to use free resolutions as an "enhanced" version of
degeneracy loci formulas. We illustrate our approach on several examples and
show how they are connected to moduli spaces of Abelian varieties. To make the
article accessible to both algebraists and geometers, we also include
background material on free resolutions and representation theory.Comment: 41 pages, uses tabmac.sty, Dedicated to David Eisenbud on the
occasion of his 65th birthday; v2: fixed some typos and added reference
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