2024 Ulrich bundles on cubic fourfolds

Ulrich bundles on cubic fourfolds

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Web25 Nov 2024 · Abstract We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of … WebThis allows to settle the Ulrich complexity problem for very general cubic fourfolds.Weknowofnopair.n;d/withn 5,d 4suchthattheUlrichcomplexity ... recall how can …

Stability conditions on Kuznetsov components of …

WebYeongrak Kim (UdS): Ulrich bundles on cubic fourfolds: 11.11.2024: Andreas Braun (Durham): String Compactifications and Arithmetic String theory gives a strong motivation for studying elliptic fibrations and Hodge cycles on K3 surfaces, as well as higher-dimensional Calabi-Yau varieties. After explaining the relevant data of the setup and ... Web25 Nov 2024 · First, we construct a simple sheaf E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an E appears as an … cost to build an ice rink

Compactification of the moduli space of minimal instantons on …

Webclassi cation of Ulrich bundles on a cubic surface, we classify the stable Ulrich bundles on a smooth quartic surface in P3 of Picard number 2 by rst Chern class. 1. Introduction and … Web1 Mar 2024 · A vector bundle E on V 5 is an (minimal) instanton bundle if and only if E (1) is an Ulrich bundle of rank 2. In addition, described the moduli space of stable Ulrich bundles of rank r. Theorem 2.21 [18, Theorem 3.11] The moduli space M r s U of stable Ulrich bundles of rank r on V 5 is a smooth (r 2 + 1)-dimensional open subscheme of M (r, r ... cost to build an ios app

A Survey of Ulrich Bundles

WebStrategy of the proofs. Our proof of Theorem 1.1 is inspired by the approach used in [] to address the corresponding question for cubic threefolds, although the situation in the case of GM threefolds is more complicated.Roughly speaking, the main issue is the presence of the rank two exceptional bundle U X $\mathcal {U}_X$, which does not allow to use the … WebCubic fourfolds IGenerically H2,2 prim (X,Z) = 0. INL d is locus of cubics where a class T ∈H4(S,Z) (of discriminant d = dischh2,Ti) becomes of type (2,2). INL d is a divisor, cut out … cost to build a new house per square footWeb30 May 2024 · The vector bundle E is an Ulrich bundle if it satisfies these equivalent conditions. Proof We first prove the theorem holds for X=\mathbb {P}. In that case (i) and (iii) just mean that the vector bundle E is trivial, and we must prove that this follows from (ii). breast clinic galway university hospital

"WebCUBIC FOURFOLDS 3 Label the projections pand qas P~5 q p / 1 2 P5; and observe that pis a P1-bundle, the projectivization of O( 1;0) O(0; 11) over P1 P . Let F 1;F 2 ˆ~P5 be the … " - Ulrich bundles on cubic fourfolds

Ulrich bundles on cubic fourfolds

WebAbstract. We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric bration and Kuznetsov’s treatment of their bounded … Web25 Nov 2024 · Abstract: We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of …

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WebBy the way, we know the existence of Ulrich bundles of huge rank in these cases from [11, 24]. Therefore, it is interesting to compute all the possible ranks of Ulrich bundles on the … Web13 Nov 2024 · Stable rationality of quadric and cubic surface bundle fourfolds. 04 April 2024. Asher Auel, Christian Böhning & Alena Pirutka. Very stable Higgs bundles, equivariant multiplicity and mirror symmetry. ... Characterization of Ulrich bundles on Hirzebruch surfaces. 08 January 2024. Vincenzo Antonelli. Higher order Jacobians, Hessians and …

http://www.mat.unimi.it/users/pertusi/CV_Pertusi.pdf WebKuznetsov showed in that for many cubic fourfolds (notably, in each case X was rational), Ku (X) $\textrm {Ku}(X)$ is equivalent to the derived category of a K3 surface. ... the notion of …

WebWe show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf \mathcal E E of rank 6 as an elementary modification of an ACM … WebEnseignement Cours – Topologie des variétés algébriques Introduction La théorie de Hodge fournit les notions de « structure de Hodge », développée par Griffiths, et de « structure de Hodge mixte » introduite par Deligne. C’est un outil puissant pour étudier la topologie des (familles de) variétés algébriques complexes et ce cours en présente les principaux …

Web1 Aug 2024 · In particular, such cubic fourfolds form a divisor in the space of cubic fourfolds, and hence the Ulrich complexity of a (very) general cubic fourfold is at least 3. …

Web3 Nov 2024 · In this paper, we classify Ulrich vector bundles that are not big on smooth complex surfaces and threefolds. cost to build an indoor poolWebclassi cation of Ulrich bundles on a cubic surface, we classify the stable Ulrich bundles on a smooth quartic surface in P3 of Picard number 2 by rst Chern class. 1. Introduction and History The study of Ulrich bundles originates in an article by Bernd Ulrich that ap-peared in 1984. In [42], Ulrich investigated criteria for a local Cohen-Macaulay breast clinic city hospitalWeb‪Università degli studi di Milano‬ - ‪‪Cited by 137‬‬ - ‪Algebraic Geometry‬ cost to build a ninja gymWebNow on home page. ads; Enable full ADS cost to build an indoor shooting rangeWebS. Feyzbakhsh, L. Pertusi, Serre-invariant stability conditions and Ulrich bundles on cubic threefolds, Epijournal de Géométrie Algébrique, Volume 7 (2024), ... M. Ornaghi, L. Pertusi, Voevodsky's conjecture for cubic fourfolds and Gushel-Mukai fourfolds via noncommutative K3 surfaces, J. Noncommut. Geom. (2)13 (2024), 499-515 . Notes. cost to build an officeWebThe birational geometry of cubic fourfolds is a fascinating and challenging problem in alge-braic geometry. The guiding principle of this paper is to understand and reinterpret geometric constructions on cubic fourfolds in terms of sheaf theory and homological algebra. 2010 Mathematics Subject Classi cation. 18E30, 14E08, 13D09. Key words and ... cost to build an iphoneWebWe show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of an ACM bundle of … cost to build an observatory