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Showing 1 to 13 of 13 for “"Complete Intersections"”.
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Notes on Some (0,2) Supersymmetric Theories in Two Dimensions
… for various spaces including Grassmannians, complete intersections in Grassmannians, and non-complete intersections such as Pfaffians. Generalizations of (2,2) Toda dual theories to (0,2) Toda-like theories are also discussed and some examples are given, including products of projective …
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Number-theoretic properties of the binomial distribution with applications in arithmetic geometry
… describe Bucur and Kedlaya's generalization to complete intersections. We then prove theorems concerning the probability that a binomial distribution yields an integer of various certain properties, such as being prime or being squarefree. Finally, we show how to apply such a theorem, concerning …
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Asymptotic Behavior of Homology and Intersection Multiplicity
… nonnegativity of intersection multiplicity over complete intersections. In the third result, we use the Frobenius endomorphism and the vanishing of Ext to characterize finitely generated modules of finite projective dimension over complete intersections. This result completes the picture as …
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Complete Mirror Pairs and Their Naive Stringy Hodge Numbers
… a pair</p><p>of Calabi-Yau complete intersections</p><p>$(Y_{\Delta_1,\dotsc,\Delta_c},Y_{\nabla_1,\dotsc,\nabla_c})$ in Gorenstein Fano</p><p>toric varieties $(X_\Delta,X_\nabla)$. These Calabi-Yau varieties are singular</p><p>in general. Batyrev and Nill have developed a …
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Positive Sasakian Structures on Links of Weighted Complete Intersection Singularities
… $(n-2)$-connected. In dimension 5, there is a complete classification of simply connected spin manifolds due to Smale. Hypersurface singularities yielding links of dimension 5 have been treated by Boyer, Galicki, Koll\'{a}r, Nakamaye, and others. This paper investigates isolated singularities …
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Betti numbers of Koszul algebras and codimension two matrix factorizations
… 3 for the defining ideals of Koszul almost complete intersections and, in the process, give an affirmative answer for all such rings to a question of Avramov, Conca, and Iyengar about the Betti numbers of Koszul algebras. In Chapter 4, we study the codimension two matrix factorizations of …
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Splitting of Vector Bundles on Punctured Spectrum of Regular Local Rings
… quotients of regular local rings have to be complete intersections. More precisely we prove that if (<em>R,</em> m) is a regular local ring of dimension at least five, p is a prime ideal of codimension two, and the ring Γ (<em>V, R/</em>p) is Gorenstein, where <em>V</em> is the open set …
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Homological invariants of some special varieties
… ideal of a variety of lines arising from a complete intersection of points. We also compute the Castelnuovo-Mumford regularity of the defining ideal of grids of lines and complete intersections of lines in P1×P1×P1. Then we study the regularity of another special variety, i.e., the edge …
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Models of genus one curves
… given as double covers of P1, plane cubics, or complete intersections of two quadrics in P3. By minimising such a curve we mean making the invariants associated to its defining equations as small as possible using a suitable change of coordinates. We study the non-uniqueness of minimisations of …
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On hochschild cohomology and modular representation theory
… a family of examples given by the quantum complete intersections where all the derivations are r-integrable. In the second part our attention is focused on the local invariants. More precisely, we fully characterise blocks B with unique isomorphism class of simple modules such that the …
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Ample subschemes and partially positive line bundles
… share several geometric properties with complete intersections of ample divisors. For example, the Lefschetz hyperplane theorem on rational cohomology holds and the cycle class of an ample subvariety is numerically positive. Using these results, we construct counterexamples to a …
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Weak Purity for Gorenstein Rings
… to recover Grothendieck's purity theorem for complete intersections in the special case of a hypersurface ring B. Applications are considered: in extensions $B\to A$ similar to those above which are normal (with Galois group G), a relationship between codimension two primes of A which are …
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Various Differents for 0-Dimensional Schemes and Applications
… for a 0-dimensional smooth scheme to be a complete intersection. We also generalize some results such as Dedekind's formula and the characterization of the Cayley-Bacharach property by using Liaison theory. In addition, several propositions on the uniformities are proven. In Chapter 5 we …