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The hyperdeterminant of a symmetric tensor
hyperdeterminant symmetric tensor Algebraic Geometry
2011/9/19
Abstract: The hyperdeterminant of a symmetric tensor factors into several irreducible factors with multiplicities. Using geometric techniques these factors are identified along with their degrees and ...
On the existence of curves with $A_k$-singularities on $K3$-surfaces
versal deformations tacnodes Severi varieties K3 surfaces Ak-singularities
2011/9/19
Abstract: Let $(S,H)$ be a general primitively polarized $K3$ surface. We prove the existence of curves in $|\mathcal O_S(nH)|$ with $A_k$-singularities and corresponding to regular points of the equi...
Families of canonically polarized manifolds over log Fano varieties
Families of canonically polarized manifolds log Fano varieties Algebraic Geometry
2011/9/19
Abstract: Let (X,D) be a dlt pair, where X is a normal projective variety. Let S denote the support of the rounddown of D, and K the canonical divisor of X. We show that any smooth family of canonical...
Gauge Theories on ALE Space and Super Liouville Correlation Functions
Gauge Theories ALE Space Super Liouville Correlation Functions High Energy Physics - Theory
2011/10/9
Abstract: We present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured ...
Flatness in non-Archimedean analytic geometry
Flatness non-Archimedean analytic geometry Algebraic Geometry
2011/9/16
Abstract: This text is devoted to the systematic study of flatness in the context of Berkovich analytic spaces. After having shown through a counter-example that naive flatness in that context is not ...
The Local Structure of Compactified Jacobians: Deformation Theory
Compactified Jacobian compactified Picard scheme nodal curve torsion-free sheaf
2011/9/16
Abstract: This paper studies the local geometry of compactified Jacobians constructed by Caporaso, Oda-Seshadri, Pandharipande, and Simpson. The main result is a presentation of the completed local ri...
On Finiteness of B-representatoin and Semi-log Canonical Abundance
Finiteness of B-representatoin Semi-log Canonical Abundance Algebraic Geometry
2011/9/16
Abstract: We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) a...
On the Demailly-Semple jet bundles of hypersurfaces in $\CP^3$
Demailly-Semple jet bundles hypersurfaces Algebraic Geometry
2011/9/15
Abstract: Let $X$ be a smooth hypersurface of degree $d$ in $\CP^3$. By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle $X_3$ of $X$, the bundle $\ocal_{X_3}(1)$ ...
Test ideals via a single alteration and discreteness and rationality of $F$-jumping numbers
test ideal alteration F-jumping number multiplier ideal
2011/9/15
Abstract: Suppose $(X, \Delta)$ is a log-$\bQ$-Gorenstein pair. Recent work of M. Blickle and the first two authors gives a uniform description of the multiplier ideal $\mJ(X;\Delta)$ (in characterist...
Birational superrigidity and slope stability of Fano manifolds
Birational superrigidity Fano manifolds Algebraic Geometry
2011/9/15
Abstract: We show a relation between the birational superrigidity of Fano manifold and its slope stability in the sense of Ross-Thomas.
Refining Castelnuovo-Halphen bounds
Castelnuovo-Halphen Theory Hartshorne-Rao module Hilbert polynomial arithmetic genus
2011/9/14
Abstract: Fix integers $r,d,s,\pi$ with $r\geq 4$, $d\gg s$, $r-1\leq s \leq 2r-4$, and $\pi\geq 0$. Refining classical results for the genus of a projective curve, we exhibit a sharp upper bound for ...
Dissimilarity maps on trees and the representation theory of $GL_n(\C)$
Dissimilarity maps trees the representation theory Algebraic Geometry
2011/9/14
Abstract: We revisit the representation theory in type $A$used previously to establish that the dissimilarity vectors of phylogenetic trees are points on the tropical Grassmannian variety. We use a di...
Standard Monomial Theory for desingularized Richardson varieties in the flag variety GL(n)/B
Standard Monomial Theory Richardson varieties Algebraic Geometry
2011/9/14
Abstract: We consider a desingularization Gamma of a Richardson variety X_w^v=X_w \cap X^v in the flag variety Fl(n)=GL(n)/B, obtained as a fibre of a projection from a certain Bott-Samelson variety Z...
Abstract: In this brief note, we show that every smooth toric variety over the field of complex numbers is an Oka manifold.
A canonical linear system associated to adjoint divisors in characteristic $p > 0$
Linear system test ideal multiplier ideal base-point-free ample characteristic p > 0
2011/9/15
Abstract: Suppose that $X$ is a projective variety over an algebraically closed field of characteristic $p > 0$. Further suppose that $L$ is an ample (or more generally in some sense positive) divisor...