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Three lectures on Algebraic Microlocal Analysis
Three lectures Algebraic Microlocal Analysis Algebraic Geometry
2012/6/27
These three lectures present some fundamental and classical aspects of microlocal analysis. Starting with the Sato's microlocalization functor and the microsupport of sheaves, we then construct a micr...
Uniruledness of some moduli spaces of stable pointed curves
Pointed curve Moduli space Uniruledness Hyperelliptic curves Complete intersection surfaces
2012/6/27
We prove uniruledness of some moduli spaces $\bar{M}_{g,n}$ of stable curves of genus $g$ with $n$ marked points using linear systems on nonsingular projective surfaces containing the general curve of...
Purity of boundaries of open complex varieties
Mixed Hodge theory of singular varieties intersection cohomology resolution of singularities
2012/6/25
We study the boundary of an open smooth complex algebraic variety $U$. We ask when the cohomology of the geometric boundary $Z=X\setminus U$ in a smooth compactification $X$ is pure with respect to th...
Jet bundles on projective space: New examples
Atiyah sequence jet bundle characteristic class generalized Atiyah class
2012/6/21
In previous papers it was shown that the left and right O-module structure of the jet bundles on the projective line differed. In this paper we show that similar statements hold for jet bundles on pro...
Existence of covers with fixed ramification in positive characteristic
Existence of covers fixed ramification positive characteristic Algebraic Geometry
2012/6/25
We discuss two elementary constructions for covers with fixed ramification in positive characteristic. As an application, we compute the number of certain classes of covers between projective lines br...
Existence of good moduli spaces for A_k-stable curves
Existence of good moduli spaces A_k-stable curves Algebraic Geometry
2012/6/25
We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a weak analog of the Keel-Mori theorem, which guarantees the existence of a coarse mo...
Classification of 2-Fano manifolds with high index
Classification of 2-Fano manifolds high index Algebraic Geometry
2012/6/27
In this paper we classify n-dimensional Fano manifolds with index >=n-2 and positive second Chern character.
Singularities of duals of Grassmannians
Singularities of duals of Grassmannians Algebraic Geometry Differential Geometry
2012/6/21
Let $X$ be a smooth irreducible nondegenerate projective variety and let $X^*$ denote its dual variety. It is well known that $\sigma_2(X)^*$, the dual of the 2-secant variety of $X$, is a component o...
A note on the unramified Brauer group of a homogeneous space
Unramified Brauer group homogeneous space linear algebraic group
2012/6/21
We give a new proof of the theorem stating that for any connected linear algebraic group G over an algebraically closed field k of characteristic 0 and for any closed connected subgroup H of G, the un...
Automorphisms of Drinfeld half-spaces over a finite field
Non-archimedean analytic geometry Berkovich spaces Drinfeld upper half-space birational transformations
2012/6/21
We show that the automorphism group of Drinfeld's half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the s...
On reductive automorphism groups of regular embeddings
reductive automorphism groups regular embeddings Algebraic Geometry
2012/6/21
Let G be a connected reductive complex algebraic group acting on a smooth complete complex algebraic variety X. We assume that X under the action of G is a regular embedding, a condition satisfied in ...
A'Campo curvature bumps and the Dirac phenomenon near a singular point
Curve-germs Curvature Newton-Puiseux Innitesimals Dirac phenomenon
2012/6/19
The level curves of an analytic function germ almost always have bumps at unexpected points near the singularity. This profound discovery of N. A'Campo is fully explored in this paper for $f(z,w)\in \...
Binary hidden Markov models and varieties
Binary hidden Markov models varieties Algebraic Geometry
2012/6/19
The technological applications of hidden Markov models have been extremely diverse and successful, including natural language processing, gesture recognition, gene sequencing, and Kalman filtering of ...
The Homotopy Sequence of Nori's Fundamental Group
The Homotopy Sequence of Nori's Fundamental Group Algebraic Geometry
2012/6/18
In this paper, we investigate the necessary sufficient conditions for the exactness of the homotopy sequence of Nori's fundamental group and apply these to various special situations to regain some cl...
Moduli of products of stable varieties
2012/6/18
We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined m...