On the motive of an algebraic surface

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August undefined, 2024

Web9 de abr. de 2024 · Abstract. In this paper, we study the Gieseker moduli space \mathcal {M}_ {1,1}^ {4,3} of minimal surfaces with p_g=q=1, K^2=4 and genus 3 Albanese … WebAuthor: Gene Freudenburg Publisher: Springer ISBN: 3662553503 Category : Mathematics Languages : en Pages : 319 Download Book. Book Description This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as …

On the Chow Motive of an algebraic surface. UMR 5582

WebOn the motive of an algebraic surface. 0.1. The theory of motives has been created by Grothendieck in order to understand better — among other things — the underlying … Web29 de jan. de 2024 · Including the basic theory of schemes and cohomology of coherent sheaves (such as R. Hartshorne’s AG chapter 2,3), the basic theory of curves and a little bit surface theory. 1. The basic theory of algebraic cycles, Chow groups and intersection theory. Chapter 1-18 in W. Fulton’s Intersection Theory. (see Intersection Theory). rcd20-110s12w

Geometry of Algebraic Curves - University of Chicago

WebThe foundations of algebraic geometry were lacking in that period, many results were not clearly formulated and proofs were not always complete. These foundations were laid in the thirties and fourties by van der Waerden, Zariski and Weil. Zariski wrote a monograph [Za] about surfaces incorporating these new techniques. WebDynamics on algebraic surfaces MPI Arbeitstagung 2007 Curtis T. McMullen In this talk we discuss connections between algebraic integers and auto-morphisms of compact complex surfaces. Integers. Conjecturally, the smallest algebraic integer λ > 1 is the root λLehmer = 1.1762808... of Lehmer’s polynomial, P(x) = 1 +x −x3 −x4 −x5 −x6 ... Web5 de abr. de 2013 · > Algebraic Cycles and Motives > On the Transcendental Part of the Motive of a Surface 7 - On the Transcendental Part of the Motive of a Surface … rcd200

[1602.06403v1] The motive of the Fano surface of lines - arXiv.org

Algebraic Surface -- from Wolfram MathWorld

WebLet G be a split, simple, simply connected, algebraic group over Q. The degree 4, weight 2 motivic cohomology group of the classifying space BG of G is identified with Z. We construct cocycles representing the generator of this group, known as the second universal motivic Chern class. If G = SL(m), there is a canonical cocycle, defined by the first author (1993). WebIntroduction 0.1. The theory of motives has been created by Grothendieck in order to under-stand better — among other things — the underlying "objects" of the cohomologygroups … rcd2071bWebThis paper looks at some results concerning the Monodromy Conjecture. The conjecture states that for a nonconstant regular function is nonsingular. This proof is not only included for its simplicity, but also because we will need exactly the same arguments in the second part. There we explain what can, and what cannot, be expected in the singular case. rcd200c

"Webi.e. there exists an algebraic correspondence between any K3 surface Sand an associated Abelian variety, the Kuga-Satake variety K(S). This would imply that the motive of any such K3 surface is Abelian, i.e. it lies in the subcategory MAb rat(C) of the (covariant) category M (C) of Chow motives generated by the motives of curves. " - On the motive of an algebraic surface

On the motive of an algebraic surface

Webmoduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to WebDivisors on a Riemann surface. A Riemann surface is a 1-dimensional complex manifold, and so its codimension-1 submanifolds have dimension 0.The group of divisors on a compact Riemann surface X is the free abelian group on the points of X.. Equivalently, a divisor on a compact Riemann surface X is a finite linear combination of points of X with …

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WebThe theory of pure motives was introduced by Grothendieck in the 1960s and since then it has become a powerful language to encode intersection-theoretic, cohomological, and arithmetic data of smooth, projective varieties. WebOn the Chow Motive of an algebraic surface. Lundi, 17 Octobre, 2005 - 16:00 Prénom de l'orateur : Claudio Nom de l'orateur : PEDRINI Résumé : Bloch's Conjecture for …

Webalgebraic curves as a smooth projective curve (given by explicit equations), and an explicit divisor, there is an algorithm to determine the space L(D). We’ll do that in a week or two. …

Web11 de mai. de 2024 · We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a motivic interpretation of a long standing conjecture of Safarevich which has been settled only recently by Buskin. The main step consists of a new proof of Safarevich's conjecture that circumvents the analytic parts in Buskin's approach, … Web2 de mai. de 2006 · On the motive of an algebraic surface Article Aug 1990 Jacob P. Murre View On a conjectural filtration on the Chow groups of an algebraic variety Part II: Verification of the conjectures for...

Web20 de fev. de 2016 · Abstract:The purpose of this note is to prove that the Chow motive of the Fano surface of lines on the smooth cubic threefold is finite-dimensional in the sense of Kimura. This gives an example of a smooth projective variety that is not dominated by a product of curves but whose Chow motive is of Abelian type. Submission history

WebAlgebraic curves is one of the oldest subjects in modern mathematics, as it was one of the rst things people did once they learned about polynomials. It has developed over time a multiplicity of language and symbols, and we will run through it. Let X be a smooth projective algebraic curve over C. rcd21WebZariski, O. (1962). The Theorem of Riemann-Roch for High Multiples of an Effective Divisor on an Algebraic Surface. The Annals of Mathematics, 76(3), 560. doi:10.2307/1970376 rcd-1knWeb11 de mai. de 2024 · We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a motivic interpretation of a long standing conjecture of … rcd158wh2Web20 de fev. de 2016 · Mathematics > Algebraic Geometry. arXiv:1602.06403 (math) [Submitted on 20 Feb 2016] ... Abstract: The purpose of this note is to prove that the Chow motive of the Fano surface of lines on the smooth cubic threefold is finite-dimensional in the sense of Kimura. rcd1884 land prideWeb1 de set. de 2024 · Journal of Algebraic Combinatorics: An International Journal Volume 56 ... Böhning C von Bothmer H-CG Katzarkov L Sosna P Determinantal Barlow surfaces and phantom categories J. Europ. Math. ... Sosna P Some remarks on phantom categories and motives Bull. Belg. Math. Soc. Simon Stevin 2024 27 3 337 352 4146735 … rcd200 bluetoothWebThis has interesting implications for mirror symmetry, as mirror symmetry exchanges the odd and even Betti numbers. Here the zeta functions for a one-parameter family of K3 surfaces, $\mathbb{P}_3[4]$, and a two-parameter family of octics in weighted projective space, $\mathbb{P}_4{}^{(1, 1, 2, 2, 2)} [8]$, are computed. rcd 2015WebDynamics and Algebraic Surfaces ; Namboodiri Lectures -- University of Chicago 20-22 January 2003 Curtis T. McMullen, Harvard University ; Lectures: Abstract I. Islands on K3 surfaces II. Random lattices and Sqrt[n] mod 1 III. Billiards ; References: Dynamics on K3 surfaces: Salem numbers and Siegel disks Gaps in Sqrt[n] mod 1 and ergodic theory rcd 204