Expand all Collapse all | Results 1 - 8 of 8 |
1. CJM 2012 (vol 64 pp. 1222)
Normality of Maximal Orbit Closures for Euclidean Quivers Let $\Delta$ be an Euclidean quiver. We prove that the closures of
the maximal orbits in the varieties of representations of $\Delta$
are normal and Cohen--Macaulay (even complete intersections).
Moreover, we give a generalization of this result for the tame
concealed-canonical algebras.
Keywords:normal variety, complete intersection, Euclidean quiver, concealed-canonical algebra Categories:16G20, 14L30 |
2. CJM 2011 (vol 65 pp. 3)
Finitely Related Algebras in Congruence Distributive Varieties Have Near Unanimity Terms We show that every finite, finitely related algebra in a congruence
distributive variety has a near unanimity term operation.
As a consequence we solve the near unanimity problem for relational
structures: it is decidable whether a given finite set of relations on
a finite set admits a compatible near unanimity operation. This
consequence also implies that it is decidable whether a given finite
constraint language defines a constraint satisfaction problem of
bounded strict width.
Keywords:congruence distributive variety, JÃ³nsson operations, near unanimity operation, finitely related algebra, constraint satisfaction problem Categories:08B05, 08B10 |
3. CJM 2011 (vol 63 pp. 616)
A Modular Quintic Calabi-Yau Threefold of Level 55 In this note we search the parameter space of Horrocks-Mumford quintic
threefolds and locate a Calabi-Yau threefold that is modular, in the
sense that the $L$-function of its middle-dimensional cohomology is
associated with a classical modular form of weight 4 and level 55.
Keywords: Calabi-Yau threefold, non-rigid Calabi-Yau threefold, two-dimensional Galois representation, modular variety, Horrocks-Mumford vector bundle Categories:14J15, 11F23, 14J32, 11G40 |
4. CJM 2008 (vol 60 pp. 961)
About the Defectivity of Certain Segre--Veronese Varieties We study the regularity of the higher secant varieties of $\PP^1\times
\PP^n$, embedded with divisors of type $(d,2)$ and $(d,3)$. We
produce, for the highest defective cases, a ``determinantal'' equation
of the secant variety. As a corollary, we prove that the Veronese
triple embedding of $\PP^n$ is not Grassmann defective.
Keywords:Waring problem, Segre--Veronese embedding, secant variety, Grassmann defectivity Categories:14N15, 14N05, 14M12 |
5. CJM 2007 (vol 59 pp. 36)
Classification of Ding's Schubert Varieties: Finer Rook Equivalence K.~Ding studied a class of Schubert varieties $X_\lambda$
in type A partial
flag manifolds, indexed by
integer partitions $\lambda$ and in bijection
with dominant permutations. He observed that the
Schubert cell structure of $X_\lambda$ is indexed by maximal rook
placements on the Ferrers board $B_\lambda$, and that the
integral cohomology groups $H^*(X_\lambda;\:\Zz)$, $H^*(X_\mu;\:\Zz)$ are
additively isomorphic exactly when the Ferrers boards $B_\lambda, B_\mu$
satisfy the combinatorial condition of \emph{rook-equivalence}.
We classify the varieties $X_\lambda$ up to isomorphism, distinguishing them
by their graded cohomology rings with integer coefficients. The crux of our approach
is studying the nilpotence orders of linear forms in
the cohomology ring.
Keywords:Schubert variety, rook placement, Ferrers board, flag manifold, cohomology ring, nilpotence Categories:14M15, 05E05 |
6. CJM 2000 (vol 52 pp. 265)
On Orbit Closures of Symmetric Subgroups in Flag Varieties We study $K$-orbits in $G/P$ where $G$ is a complex connected
reductive group, $P \subseteq G$ is a parabolic subgroup, and $K
\subseteq G$ is the fixed point subgroup of an involutive
automorphism $\theta$. Generalizing work of Springer, we
parametrize the (finite) orbit set $K \setminus G \slash P$ and we
determine the isotropy groups. As a consequence, we describe the
closed (resp. affine) orbits in terms of $\theta$-stable
(resp. $\theta$-split) parabolic subgroups. We also describe the
decomposition of any $(K,P)$-double coset in $G$ into
$(K,B)$-double cosets, where $B \subseteq P$ is a Borel subgroup.
Finally, for certain $K$-orbit closures $X \subseteq G/B$, and for
any homogeneous line bundle $\mathcal{L}$ on $G/B$ having nonzero
global sections, we show that the restriction map $\res_X \colon
H^0 (G/B, \mathcal{L}) \to H^0 (X, \mathcal{L})$ is surjective and
that $H^i (X, \mathcal{L}) = 0$ for $i \geq 1$. Moreover, we
describe the $K$-module $H^0 (X, \mathcal{L})$. This gives
information on the restriction to $K$ of the simple $G$-module $H^0
(G/B, \mathcal{L})$. Our construction is a geometric analogue of
Vogan and Sepanski's approach to extremal $K$-types.
Keywords:flag variety, symmetric subgroup Categories:14M15, 20G05 |
7. CJM 1998 (vol 50 pp. 1253)
Integral representation of $p$-class groups in ${\Bbb Z}_p$-extensions and the Jacobian variety For an arbitrary finite Galois $p$-extension $L/K$ of
$\zp$-cyclotomic number fields of $\CM$-type with Galois group $G =
\Gal(L/K)$ such that the Iwasawa invariants $\mu_K^-$, $ \mu_L^-$
are zero, we obtain unconditionally and explicitly the Galois
module structure of $\clases$, the minus part of the $p$-subgroup
of the class group of $L$. For an arbitrary finite Galois
$p$-extension $L/K$ of algebraic function fields of one variable
over an algebraically closed field $k$ of characteristic $p$ as its
exact field of constants with Galois group $G = \Gal(L/K)$ we
obtain unconditionally and explicitly the Galois module structure
of the $p$-torsion part of the Jacobian variety $J_L(p)$ associated
to $L/k$.
Keywords:${\Bbb Z}_p$-extensions, Iwasawa's theory, class group, integral representation, fields of algebraic functions, Jacobian variety, Galois module structure Categories:11R33, 11R23, 11R58, 14H40 |
8. CJM 1997 (vol 49 pp. 675)
Some adjunction-theoretic properties of codimension two non-singular subvarities of quadrics We make precise the structure of the first two reduction morphisms
associated with codimension two non-singular subvarieties
of non-singular quadrics $\Q^n$, $n\geq 5$.
We give a coarse classification of the same class of subvarieties
when they are assumed not to be of log-general-type.}
Keywords:Adjunction Theory, classification, codimension two, conic bundles,, low codimension, non log-general-type, quadric, reduction, special, variety. Categories:14C05, 14E05, 14E25, 14E30, 14E35, 14J10 |