848 research outputs found
Resolutions and cohomology over complete intersections
This chapter contains a new proof and new applications of a theorem of Shamash and Eisenbud, providing a construction of projective resolutions of modules over a complete intersection. The duals of these infinite projective resolutions are finitely generated differential graded modules over a graded polynomial ring, so they can be represented in the computer, and can be used to compute Ext modules simultaneously in all homological degrees. It is shown how to write Macaulay 2 code to implement the construction, and how to use the computer to determine invariants of modules over complete intersections that are difficult to obtain otherwise
Absolutely Koszul algebras and the Backelin-Roos property
We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos
property and their behavior under standard algebraic operations. In particular,
we identify some Veronese subrings of polynomial rings that have the
Backelin-Roos property and conjecture that the list is indeed complete. Among
other things, we prove that every universally Koszul ring defined by monomials
has the Backelin-Roos property
Shapes of free resolutions over a local ring
We classify the possible shapes of minimal free resolutions over a regular
local ring. This illustrates the existence of free resolutions whose Betti
numbers behave in surprisingly pathological ways. We also give an asymptotic
characterization of the possible shapes of minimal free resolutions over
hypersurface rings. Our key new technique uses asymptotic arguments to study
formal Q-Betti sequences.Comment: 14 pages, 1 figure; v2: sections have been reorganized substantially
and exposition has been streamline
Winter frost resistance of grapevine varieties belonging to different ecological and geographical groups
The influence of frost temperatures on survival of the buds was investigated in situ during 3 winters. The behavior of 375 grapevine varieties belonging to different ecological-geographical groups was studied at 3 locations. The rate of buds killed by frost ranged from 5.4 to 100%. The varieties of the group convar. occiclentalis exhibited the greatest frost resistance of buds during 3 winters with very low temperatures. In this group the percentage of killed buds was significantly lower than in the group convar. pontica and much less than in the group convar. orientalis
Modern Approaches in Injuries of the Larynx
Introduction: Early diagnosis and proper treatment of laryngeal trauma is of great importance for the patient to prevent the formation of stenosis in a later stage, changes in breathing and voice quality.Material and methods: The covered laryngeal trauma is a relatively rare injury. Its incidence is estimated at 1 in 30,000 visits to emergency rooms.Results: Due to their relatively low frequency and association with other life-threatening injuries, laryngeal trauma often go unrecognized. This is bad because the glottis laryngeal stenosis and insufficiency are the end result of delayed or inadequate treatment of laryngeal trauma.Conclusion: Despite the great variety of these injuries, correct diagnosis and understanding of each case justify the adoption of a standardized method for classifying and treating these injuries. These preconditions will facilitate successful therapy
Three flavors of extremal Betti tables
We discuss extremal Betti tables of resolutions in three different contexts.
We begin over the graded polynomial ring, where extremal Betti tables
correspond to pure resolutions. We then contrast this behavior with that of
extremal Betti tables over regular local rings and over a bigraded ring.Comment: 20 page
Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension
Let be a local ring, and let and be finitely generated
-modules such that has finite complete intersection dimension. In this
paper we define and study, under certain conditions, a pairing using the
modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand
diference. We exploit this pairing to examine the number of consecutive
vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all
. Our results recover and improve on most of the known bounds in the
literature, especially when has dimension at most two
(Contravariant) Koszul duality for DG algebras
A DG algebras over a field with connected and
has a unique up to isomorphism DG module with . It is proved
that if is degreewise finite, then RHom_A(?,K): D^{df}_{+}(A)^{op}
\equiv D_{df}^{+}}(RHom_A(K,K)) is an exact equivalence of derived categories
of DG modules with degreewise finite-dimensional homology. It induces an
equivalences of and the category of perfect DG
-modules, and vice-versa. Corresponding statements are proved also
when is simply connected and .Comment: 33 page
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