scholarly journals Seshadri constants on some Quot schemes

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chandranandan Gangopadhyay ◽  
Krishna Hanumanthu ◽  
Ronnie Sebastian
Keyword(s):  
Vector Bundle ◽  
Positive Integer ◽  
Line Bundles ◽  
Seshadri Constants ◽  
Quot Scheme ◽  
Quot Schemes ◽  
Grassmann Bundle

Abstract Let E be a vector bundle of rank n on ℙ 1 {\mathbb{P}^{1}} . Fix a positive integer d. Let 𝒬 ⁢ ( E , d ) {\mathcal{Q}(E,d)} denote the Quot scheme of torsion quotients of E of degree d and let Gr ⁢ ( E , d ) {\mathrm{Gr}(E,d)} denote the Grassmann bundle that parametrizes the d-dimensional quotients of the fibers of E. We compute Seshadri constants of ample line bundles on 𝒬 ⁢ ( E , d ) {\mathcal{Q}(E,d)} and Gr ⁢ ( E , d ) {\mathrm{Gr}(E,d)} .

scholarly journals Irreducibility of Lagrangian Quot schemes over an algebraic curve

2021 ◽  
Author(s):  
Daewoong Cheong ◽  
Insong Choe ◽  
George H. Hitching
Keyword(s):  
Vector Bundle ◽  
Symplectic Form ◽  
Algebraic Curve ◽  
Smooth Curve ◽  
Generic Element ◽  
Quot Scheme ◽  
Quot Schemes ◽  
Rank 2 ◽  
Complex Projective

AbstractLet C be a complex projective smooth curve and W a symplectic vector bundle of rank 2n over C. The Lagrangian Quot scheme $$LQ_{-e}(W)$$ L Q - e ( W ) parameterizes subsheaves of rank n and degree $$-e$$ - e which are isotropic with respect to the symplectic form. We prove that $$LQ_{-e}(W)$$ L Q - e ( W ) is irreducible and generically smooth of the expected dimension for all large e, and that a generic element is saturated and stable.

scholarly journals Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Svetlana Ermakova
Keyword(s):  
Vector Bundle ◽  
Complete Intersection ◽  
Finite Rank ◽  
Vector Bundles ◽  
Complete Intersections ◽  
Finite Codimension ◽  
Line Bundles ◽  
Direct Sum ◽  
Rank Vector

AbstractIn this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem.We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.

scholarly journals ON THE VOEVODSKY MOTIVE OF THE MODULI STACK OF VECTOR BUNDLES ON A CURVE

2020 ◽  
Author(s):  
Victoria Hoskins ◽  
Simon Pepin Lehalleur
Keyword(s):  
Vector Bundles ◽  
Intersection Theory ◽  
Line Bundles ◽  
Projective Curve ◽  
Classifying Space ◽  
Smooth Projective Curve ◽  
Quot Schemes ◽  
Homotopy Colimit ◽  
Moduli Stack ◽  
Fixed Rank

Abstract We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky’s category of motives. We prove that this motive can be written as a homotopy colimit of motives of smooth projective Quot schemes of torsion quotients of sums of line bundles on the curve. When working with rational coefficients, we prove that the motive of the stack of bundles lies in the localizing tensor subcategory generated by the motive of the curve, using Białynicki-Birula decompositions of these Quot schemes. We conjecture a formula for the motive of this stack, inspired by the work of Atiyah and Bott on the topology of the classifying space of the gauge group, and we prove this conjecture modulo a conjecture on the intersection theory of the Quot schemes.

scholarly journals On the Seshadri constants of adjoint line bundles

2010 ◽  
Vol 135 (1-2) ◽  
pp. 215-228 ◽  
Author(s):  
Thomas Bauer ◽  
Tomasz Szemberg
Keyword(s):  
Line Bundles ◽  
Seshadri Constants

ON THE COTANGENT SHEAF OF QUOT-SCHEMES

1998 ◽  
Vol 09 (04) ◽  
pp. 513-522 ◽  
Author(s):  
MANFRED LEHN
Keyword(s):  
Moduli Space ◽  
Short Note ◽  
Quot Scheme ◽  
Quot Schemes ◽  
Universal Family ◽  
Stable Sheaves

It is the purpose of this short note to give a global description of the cotangent sheaf of Grothendieck's Quot-scheme in terms of a relative Ext-sheaf of the universal subsheaf and the universal quotient sheaf. As an application one gets a description of the cotangent sheaf of the moduli space of stable sheaves in terms of a relative Ext-sheaf involving only a universal family in case such a family exists.

scholarly journals Projective Bundles on Infinite-Dimensional Complex Spaces

2004 ◽  
Vol 11 (1) ◽  
pp. 43-48
Author(s):  
E. Ballico
Keyword(s):  
Banach Space ◽  
Vector Bundle ◽  
Holomorphic Vector Bundle ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Infinite Dimensional ◽  
Complex Spaces ◽  
Projective Bundles ◽  
Holomorphic Embeddings ◽  
Holomorphic Line Bundles

Abstract Let V be a complex localizing Banach space with countable unconditional basis and E a rank r holomorphic vector bundle on P(V). Here we study the holomorphic embeddings of P(E) into products of projective spaces and the holomorphic line bundles on P(E). In particular we prove that if r ≥ 3, then H 1(P(E), L) = 0 for every holomorphic line bundle L on P(E).

scholarly journals Universal Series for Hilbert Schemes and Strange Duality

2018 ◽  
Vol 2020 (10) ◽  
pp. 3130-3152
Author(s):  
Drew Johnson
Keyword(s):  
Combinatorial Proof ◽  
Line Bundles ◽  
Del Pezzo Surfaces ◽  
Hilbert Schemes ◽  
Euler Characteristics ◽  
Quot Scheme ◽  
Del Pezzo ◽  
Complex Projective ◽  
Strange Duality ◽  
Projective Surfaces

Abstract We show how the “finite Quot scheme method” applied to Le Potier’s strange duality on del Pezzo surfaces leads to conjectures (valid for all smooth complex projective surfaces) relating two sets of universal power series on Hilbert schemes of points on surfaces: those for top Chern classes of tautological sheaves and those for Euler characteristics of line bundles. We have verified these predictions computationally for low order. We then give an analysis of these conjectures in small ranks. We also give a combinatorial proof of a formula predicted by our conjectures: the top Chern class of the tautological sheaf on $S^{[n]}$ associated to the structure sheaf of a point is equal to $(-1)^n$ times the nth Catalan number.

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