Given a general ternary form f=f(x_1,x_2,x_3) of degree 4 over an algebraically closed field characteristic zero, we use the geometry K3 surfaces and van den Bergh's correspondence between representations generalized Clifford algebra C_f associated to f Ulrich bundles on surface X_f:={w^4=f(x_1,x_2,x_3)} \subseteq {P}^3 construct positive-dimensional family 8-dimensional irreducible C_f. The main part our construction, which is independent interest, uses recent work Aprodu-Farkas Green's...

We propose a general definition of mathematical instanton bundle with given charge on any Fano threefold extending the classical definitions $\mathbb P^3$ and cyclic Picard group. Then we deal case blow up at point, giving an explicit construction bundles satisfying some important extra properties: moreover, also show that they correspond to smooth points component moduli space.

We prove that every Ulrich bundle on the Veronese surface has a resolution in terms of twists trivial over $\mathbb{P}^{2}$. Using this classification, we existence results for stable bundles $\mathbb{P}^{k}$ with respect to an arbitrary polarization $dH$.

In the 9th century, parts of Eutocius’ commentary on Book II Archimedes’ Sphere and Cylinder were translated into Arabic. Most extant manuscripts these trans- lations contain only fragments. However, one manuscript, Escorial, Árabe 960, contains longest known Arabic text commentary, at 41 folios long. Comparison with Greek reveals that in Escorial 960 is composed translations two disjoint II.1 II.4. A comparison various mathematical terms used parts, which I call Text B, shows they differ...

Let $G$ be $Sl_n, Sp(2n)$ or SO(2n). We consider the moduli space $M$ of semistable principal $G$-bundles over a curve $X$. Our main result is that if $U$ Zariski open subset then there no universal bundle on $U\times X$.

Given a fixed binary form f(u,v) of degree d over field k, the associated Clifford algebra is k-algebra Cf=k{u,v}/I, where I two-sided ideal generated by elements (αu+βv)d−f(α,β) with α and β arbitrary in k. All representations Cf have dimensions that are multiples d, occur families. In this article, we construct fine moduli spaces U=Uf,r for irreducible rd-dimensional each r≥2. Our construction starts projective curve defined equation wd=f(u,v), produces Uf,r as quasiprojective variety...

Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field characteristic zero, we use the geometry K3 surfaces to construct certain positive-dimensional family irreducible representations generalized Clifford algebra associated $f.$ From this obtain existence linear Pfaffian quartic surface $X_f=\{w^4=f(x_1,x_2,x_3)\},$ as well information on Brill-Noether theory general smooth curve in system $|\mathcal{O}_{X_f}(3)|.$

Abstract We use a correspondence between Ulrich bundles on projective variety and quiver representations to prove that certain del Pezzo surfaces satisfy the trichotomy, for any given polarization.

In this article, we provide an overview of a one-to-one correspondence between representations the generalized Clifford algebra $C_f$ ternary cubic form $f$ and certain vector bundles (called Ulrich bundles) on surface $X$. We study general properties bundles, using recent classification Casanellas Hartshorne, deduce existence irreducible every possible dimension.

In this note, we prove that there exist stable Ulrich bundles of every even rank on a smooth quartic surface $X \subset \mathbb{P}^3$ with Picard number 1.

Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field characteristic zero, we use the geometry K3 surfaces and van den Bergh's correspondence between representations generalized Clifford algebra $C_f$ associated to $f$ Ulrich bundles on surface $X_f:=\{w^{4}=f(x_1,x_2,x_3)\} \subseteq \mathbb{P}^3$ construct positive-dimensional family irreducible $C_f.$ The main part our construction, which is independent interest, uses recent work...

We consider regularly stable parabolic symplectic and orthogonal bundles over an irreducible smooth projective curve algebraically closed field of characteristic zero. The morphism from the moduli stack such to its coarse space is a $\mu_2$-gerbe. study period index this gerbe, solve corresponding period-index problem.

Given a fixed binary form $f(u,v)$ of degree $d$ over field $k$, the associated \emph{Clifford algebra} is $k$-algebra $C_f=k\{u,v\}/I$, where $I$ two-sided ideal generated by elements $(\alpha u+\beta v)^{d}-f(\alpha,\beta)$ with $\alpha$ and $\beta$ arbitrary in $k$. All representations $C_f$ have dimensions that are multiples $d$, occur families. In this article we construct fine moduli spaces $U=U_{f,r}$ for irreducible $rd$-dimensional each $r \geq 2$. Our construction starts projective...

In this article, we use a correspondence between Ulrich bundles on projective variety and quiver representations to prove that certain del Pezzo surfaces satisfy the trichotomy, for any given polarization.

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