We study semistable sheaves of rank 2 with Chern classes c1=0, c2=2 and c3=0 on the Fano 3-fold V5 of Picard number 1, degree 5 and index 2. We show that the moduli space of such sheaves has a ...component that is isomorphic to P5 by identifying it with the moduli space of semistable quiver representations. This provides a natural smooth compactification of the moduli space of minimal instantons, as well as Ulrich bundles of rank 2 on V5.
We prove a dichotomy for o‐minimal fields R$\mathcal {R}$, expanded by a T$T$‐convex valuation ring (where T$T$ is the theory of R$\mathcal {R}$) and a compatible monomial group. We show that if T$T$ ...is power bounded, then this expansion of R$\mathcal {R}$ is model complete (assuming that T$T$ is), it has a distal theory, and the definable sets are geometrically tame. On the other hand, if R$\mathcal {R}$ defines an exponential function, then the natural numbers are externally definable in our expansion, precluding any sort of model‐theoretic tameness.
A PROOF OF BEAL'S CONJECTURE Katsanevakis, Georgios
International journal of mathematics, game theory, and algebra,
07/2021, Letnik:
30, Številka:
4
Journal Article
If it's true that... for specific natural numbers, x, y, z, a, b, c, where a, b, c, > 2, then oi x, y, z they definitely have one thing in common. It is a generalization of Fermat's conjecture (today ...theorem).(ProQuest: ... denotes formula omitted.)
Given a real abelian field F with group G and an odd prime number ℓ, we define the circular subgroup of the pro-ℓ-group of logarithmic units and we show that for any Galois morphism ρ from the ...pro-ℓ-group of logarithmic units to Zℓ G , the image of the circular subgroup annihilates the ℓ-group of logarithmic classes. We deduce from this a proof of a logarithmic version of Solomon conjecture.
Étant donnés un corps abélien réel F de groupe G et un nombre premier impair ℓ, nous définissons le sous-groupe circulaire du pro-ℓ-groupe des unités logarithmiques et nous montrons que pour tout morphisme galoisien ρ du groupe des unités logarithmiques dans Zℓ G , l'image du sous-groupe circulaire annule le ℓ-groupe des classes logarithmiques. Nous en déduisons une preuve de l'analogue logarithmique de la conjecture de Solomon.
Generalizing a result of 15 for modular forms of level one, we give a closed formula for the sum of all Hecke eigenforms on $\Gamma_0(N)$, multiplied by their odd period polynomials in two variables, ...as a single product of Jacobi theta series for any squarefree level $N$ . We also show that for $N = 2, 3$ and $5$ this formula completely determines the Fourier expansions all Hecke eigenforms of all weights on $\Gamma_0(N)$.
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