16,312 research outputs found
Homology of generalized partition posets
We define a poset of partitions associated to an operad. We prove that the
operad is Koszul if and only if the poset is Cohen-Macaulay.
In one hand, this characterisation allows us to compute the homology of the
poset. This homology is given by the Koszul dual operad. On the other hand, we
get new methods for proving that an operad is Koszul.Comment: Final version. To appear in JPA
Derived Categories of Nodal Algebras
In this article we classify indecomposable objects of the derived categories
of finitely-generated modules over certain infinite-dimensional algebras. The
considered class of algebras (which we call nodal algebras) contains such
well-known algebras as the complete ring of a double nodal point
\kk[[x,y]]/(xy) and the completed path algebra of the Gelfand quiver. As a
corollary we obtain a description of the derived category of Harish-Chandra
modules over . We also give an algorithm, which allows to
construct projective resolutions of indecomposable complexes. In the appendix
we prove the Krull-Schmidt theorem for homotopy categories
A somewhat gentle introduction to differential graded commutative algebra
Differential graded (DG) commutative algebra provides powerful techniques for
proving theorems about modules over commutative rings. These notes are a
somewhat colloquial introduction to these techniques. In order to provide some
motivation for commutative algebraists who are wondering about the benefits of
learning and using these techniques, we present them in the context of a recent
result of Nasseh and Sather-Wagstaff. These notes were used for the course
"Differential Graded Commutative Algebra" that was part of the Workshop on
Connections Between Algebra and Geometry held at the University of Regina, May
29--June 1, 2012.Comment: 78 page
The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense
Let be the coarse moduli space of CY manifolds arising
from a crepant resolution of double covers of branched along
hyperplanes in general position. We show that the monodromy group of a
good family for is Zariski dense in the corresponding
symplectic or orthogonal group if . In particular, the period map does
not give a uniformization of any partial compactification of the coarse moduli
space as a Shimura variety whenever . This disproves a conjecture of
Dolgachev. As a consequence, the fundamental group of the coarse moduli space
of ordered points in is shown to be large once it is not a
point. Similar Zariski-density result is obtained for moduli spaces of CY
manifolds arising from cyclic covers of branched along
hyperplanes in general position. A classification towards the geometric
realization problem of B. Gross for type bounded symmetric domains is
given.Comment: 48 page
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