14 results
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2. Proof of the Kresch-Tamvakis conjecture.
- Author
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Caughman, John S. and Terada, Taiyo S.
- Subjects
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LOGICAL prediction , *INTEGERS , *MATHEMATICS , *ABSOLUTE value - Abstract
In this paper we resolve a conjecture of Kresch and Tamvakis [Duke Math. J. 110 (2001), pp. 359–376]. Our result is the following. Theorem : For any positive integer D and any integers i,j (0\leq i,j \leq D), \; the absolute value of the following hypergeometric series is at most 1: \begin{equation*} {_4F_3} \left [ \begin {array}{c} -i, \; i+1, \; -j, \; j+1 \\ 1, \; D+2, \; -D \end{array} ; 1 \right ]. \end{equation*} To prove this theorem, we use the Biedenharn-Elliott identity, the theory of Leonard pairs, and the Perron-Frobenius theorem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. Retract conjecture on a sublattice of monoidal posets.
- Author
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Kato, Ryo
- Subjects
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LOGICAL prediction , *MATHEMATICS , *PARTIALLY ordered sets , *GENERALIZATION - Abstract
Hovey and Palmieri [ The structure of the Bousfield lattice , Amer. Math. Soc., Providence, RI, 1999] proposed the retract conjecture on the Bousfield lattice of the stable homotopy category. The author, Shimomura and Tatehara [Publ. Res. Inst. Math. Sci. 50 (2014), pp. 497–513] defined the notion of monoidal posets as a generalization of the Bousfield lattice. In this paper, we prove that an analogue of the retract conjecture holds on a sublattice of monoidal posets. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
4. Volume of the Minkowski sums of star-shaped sets.
- Author
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Fradelizi, Matthieu, Lángi, Zsolt, and Zvavitch, Artem
- Subjects
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ISOPERIMETRIC inequalities , *LOGICAL prediction , *INTEGERS , *MATHEMATICS , *GENERALIZATION - Abstract
For a compact set A \subset \mathbb {R}^d and an integer k\ge 1, let us denote by \begin{equation*} A[k] = \left \{a_1+\cdots +a_k: a_1, \ldots, a_k\in A\right \}=\sum _{i=1}^k A \end{equation*} the Minkowski sum of k copies of A. A theorem of Shapley, Folkmann and Starr (1969) states that \frac {1}{k}A[k] converges to the convex hull of A in Hausdorff distance as k tends to infinity. Bobkov, Madiman and Wang [ Concentration, functional inequalities and isoperimetry , Amer. Math. Soc., Providence, RI, 2011] conjectured that the volume of \frac {1}{k}A[k] is nondecreasing in k, or in other words, in terms of the volume deficit between the convex hull of A and \frac {1}{k}A[k], this convergence is monotone. It was proved by Fradelizi, Madiman, Marsiglietti and Zvavitch [C. R. Math. Acad. Sci. Paris 354 (2016), pp. 185–189] that this conjecture holds true if d=1 but fails for any d \geq 12. In this paper we show that the conjecture is true for any star-shaped set A \subset \mathbb {R}^d for d=2 and d=3 and also for arbitrary dimensions d \ge 4 under the condition k \ge (d-1)(d-2). In addition, we investigate the conjecture for connected sets and present a counterexample to a generalization of the conjecture to the Minkowski sum of possibly distinct sets in \mathbb {R}^d, for any d \geq 7. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
5. GEOMETRIC WALDSPURGER PERIODS II.
- Author
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LYSENKO, SERGEY
- Subjects
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EISENSTEIN series , *GEOMETRIC modeling , *LOGICAL prediction , *MATHEMATICS - Abstract
In this paper we extend the calculation of the geometric Waldspurger periods from our paper [Compos. Math. 144 (2008), no. 2, 377-438] to the case of ramified coverings. We give some applications to the study of Whittaker coeffcients of the theta-lifting of automorphic sheaves from PGL2 to the metaplectic group SL2; they agree with our conjectures from [Geometric Whittaker models and Eisenstein series for Mp2, arXiv:1221.1596]. In the process of the proof, we construct some new automorphic sheaves for GL2 in the ramified setting. We also formulate stronger conjectures about Waldspurger periods and geometric theta-lifting for the dual pair (SL2, PGL2). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
6. On the constant scalar curvature Kahler metrics (II)---Existence results.
- Author
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Chen, Xiuxiong and Cheng, Jingrui
- Subjects
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CURVATURE , *GEODESIC distance , *MATHEMATICS , *GEODESICS , *LOGICAL prediction - Abstract
In this paper, we apply our previous estimates in Chen and Cheng [ On the constant scalar curvature Kähler metrics (I): a priori estimates , Preprint] to study the existence of cscK metrics on compact Kähler manifolds. First we prove that the properness of K-energy in terms of L1 geodesic distance d1 in the space of Kähler potentials implies the existence of cscK metrics. We also show that the weak minimizers of the K-energy in (E1, d1) are smooth cscK potentials. Finally we show that the non-existence of cscK metric implies the existence of a destabilized L1 geodesic ray where the K-energy is non-increasing, which is a weak version of a conjecture by Donaldson. The continuity path proposed by Xiuxiong Chen [Ann. Math. Qué. 42 (2018), pp. 69–189] is instrumental in the above proofs. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
7. Maximally algebraic potentially irrational cubic fourfolds.
- Author
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Laza, Radu
- Subjects
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LOGICAL prediction , *IRRATIONAL numbers , *MATHEMATICS , *GEOMETRY - Abstract
A well known conjecture due to Hassett asserts that a cubic fourfold X whose transcendental cohomology TX cannot be realized as the transcendental cohomology of a K3 surface is irrational. Since the geometry of cubic fourfolds is intricately related to the existence of algebraic 2-cycles on them, it is natural to ask for the most algebraic cubic fourfolds X to which this conjecture is still applicable. In this paper, we show that for an appropriate "algebraicity index" κX ∈ Q+, there exists a unique class of cubics maximizing κX, not having an associated K3 surface; namely, the cubic fourfolds with an Eckardt point (previously investigated in by Laza, Pearlstein, and Zhang [Adv. Math. 340 (2018), pp. 684-722]). Arguably, they are the most algebraic conjecturally irrational cubic fourfolds, and thus a good testing ground for Hassett's irrationality conjecture for cubic fourfolds. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
8. A CONTAINMENT RESULT IN Pn AND THE CHUDNOVSKY CONJECTURE.
- Author
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DUMNICKI, MARCIN and TUTAJ-GASIŃSKA, HALSZKA
- Subjects
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MANIFOLDS (Mathematics) , *DIFFERENTIAL geometry , *MATHEMATICS , *LOGICAL prediction , *SET theory - Abstract
In this paper we prove the containment I(nm) ⊂ M(n-1)mIm, for a radical ideal I of s general points in Pn, where s ≥ 2n. As a corollary we get that the Chudnovsky Conjecture holds for a very general set of at least 2n points in Pn. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
9. EXPECTED DIMENSIONS OF HIGHER-RANK BRILL-NOETHER LOCI.
- Author
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NAIZHEN ZHANG
- Subjects
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NOETHER'S theorem , *LOCUS (Mathematics) , *MATHEMATICS , *MATHEMATICS theorems , *CANONICAL transformations , *LOGICAL prediction - Abstract
In this paper, we prove a new expected dimension formula for certain rank two Brill-Noether loci with fixed special determinant. This answers a question asked by Osserman and also leads to a new and much simpler proof of a theorem in his 2015 work. Our result generalizes the well-known result by Bertram, Feinberg and independently Mukai on expected dimension of rank two Brill-Noether loci with canonical determinant and partially verifies a conjecture (in rank two) of Grzegorczyk and Newstead on coherent systems. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
10. TUNNEL NUMBER ONE KNOTS, m-SMALL KNOTS AND THE MORIMOTO CONJECTURE.
- Author
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GUOQIU YANG, XUNBO YIN, and FENGCHUN LEI
- Subjects
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KNOT theory , *ONE (The number) , *LOGICAL prediction , *MATHEMATICAL formulas , *MATHEMATICS - Abstract
In the present paper, we show that the Morimoto Conjecture on the super additivity of the tunnel numbers of knots in S3 is true for knots K1,K2 in S3 in which each Ki is either a tunnel number one or m-small, i = 1, 2. This extends two known results by Morimoto. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
11. ALGORITHMIC PROOF OF THE EPSILON CONSTANT CONJECTURE.
- Author
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BLEY, WERNER and DEBEERST, RUBEN
- Subjects
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GALOIS theory , *GROUP theory , *NUMBER theory , *LOGICAL prediction , *MATHEMATICS - Abstract
In this paper we will algorithmically prove the global epsilon constant conjecture for all Galois extensions L/Q of degree at most 15. In fact, we will obtain a slightly more general result whose proof is based on an algorithmic proof of the local epsilon constant conjecture for Galois extensions E/Qp of small degree. To this end we will present an efficient algorithm for the computation of local fundamental classes and address several other problems arising in the algorithmic proof of the local conjecture. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
12. STANLEY DEPTH OF POWERS OF THE EDGE IDEAL OF A FOREST.
- Author
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POURNAKI, M. R., FAKHARI, S. A. SEYED, and YASSEMI, S.
- Subjects
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POLYNOMIAL rings , *MATHEMATICAL variables , *FORESTS & forestry , *DIAMETER , *LOGICAL prediction , *MATHEMATICS - Abstract
Let K be a field and S = K[x1, . . .,xn] be the polynomial ring in n variables over the field K. Let G be a forest with p connected components G1, . . .,Gp and let I = I(G) be its edge ideal in S. Suppose that di is the diameter of Gi, 1 ≤ i ≤ p, and consider d = max{di | 1 ≤ i ≤ p}. Morey has shown that for every t ≥ 1, the quantity max{...} is a lower bound for depth(S/It). In this paper, we show that for every t ≥ 1, the mentioned quantity is also a lower bound for sdepth(S/It). By combining this inequality with Burch's inequality, we show that any sufficiently large powers of edge ideals of forests are Stanley. Finally, we state and prove a generalization of our main theorem. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
13. ON THE "MAIN CONJECTURE" OF EQUIVARIANT IWASAWA THEORY.
- Author
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RITTER, JÜRGEN and WEISS, ALFRED
- Subjects
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IWASAWA theory , *LOGICAL prediction , *MATHEMATICS , *MATHEMATICIANS , *ALGEBRAIC fields - Abstract
The article discusses the key concerns in the main conjecture of equivariant Iwasawa theory. The Lifted Root Number suggests a refinement of the Main Conjecture of classical Iwasawa theory. The article is based on classical works done by Iwasawa, Kubota, Leopoldt, Greenberg, Ferrero Washington, and Mazur Wiles. The authors present theorems and proofs in this paper to further explain their findings.
- Published
- 2011
- Full Text
- View/download PDF
14. The Auslander-Reiten conjecture for Gorenstein rings.
- Subjects
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GORENSTEIN rings , *COMMUTATIVE rings , *LOGICAL prediction , *ALGEBRAIC fields , *MATHEMATICS - Abstract
The Nakayama conjecture is one of the most important conjectures in ring theory. The Auslander-Reiten conjecture is closely related to it. The purpose of this paper is to show that if the Auslander-Reiten conjecture holds in codimension one for a commutative Gorenstein ring $R$, then it holds for $R$. [ABSTRACT FROM AUTHOR]
- Published
- 2008
- Full Text
- View/download PDF
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