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pro vyhledávání: '"14h60"'
Autor:
Hong, Jiuzu, Yu, Huanhuan
The coherence conjecture of Pappas and Rapoport, proved by Zhu, asserts the equality of dimensions for the global sections of a line bundle over a spherical Schubert variety in the affine Grassmannian and those of another line bundle over a certain u
Externí odkaz:
http://arxiv.org/abs/2412.15062
Generalizing the Martens theorem for line bundles over a curve $C$, we obtain upper bounds on the dimension of the Brill--Noether locus $B^k_{n, d}$ parametrizing stable bundles of rank $n \ge 2$ and degree $d$ over $C$ with at least $k$ independent
Externí odkaz:
http://arxiv.org/abs/2412.12719
Let $X$ be a smooth geometrically connected projective curve of genus at least 2 over a field of characteristic zero. We compute the essential dimension of the moduli stack of symplectic bundles over $X$. Unlike the case of vector bundles, we are abl
Externí odkaz:
http://arxiv.org/abs/2412.05375
Autor:
Watanabe, Kenta
Let $X$ be a K3 surface, let $C$ be a smooth curve of genus $g$ on $X$, and let $A$ be a base point free and primitive line bundle $g_d^r$ on $C$ with $d\geq4$ and $r\geq\sqrt{\frac{d}{2}}$. In this paper, we prove that if $g>2d-3+(r-1)^2$, then ther
Externí odkaz:
http://arxiv.org/abs/2412.02256
Autor:
Jiang, Chen, Ren, Peng
We give a criterion for slope-stability of the syzygy bundle of a globally generated ample line bundle on a smooth projective variety of Picard number $1$ in terms of Hilbert polynomial. As applications, we prove the stability of syzygy bundles on ma
Externí odkaz:
http://arxiv.org/abs/2412.00476
Autor:
Pine, Jagadish
In this short note, we provide an alternative proof of a notable theorem by Narasimhan and Ramanan. The theorem states that the moduli space of $S$-equivalence classes of semistable rank $2$ vector bundles over a curve $X$ of genus $2$ with trivial d
Externí odkaz:
http://arxiv.org/abs/2411.15774
Autor:
Chern, Shane
In this paper, we establish simple $k$-fold summation expressions for the Quot and motivic Cohen--Lenstra zeta functions associated with the $(2,2k)$ torus links. Such expressions lead us to some multiple Rogers--Ramanujan type identities and their f
Externí odkaz:
http://arxiv.org/abs/2411.07198
Autor:
Debarre, Olivier
We discuss a conjecture made by Alexander Polishchuk and David Kazhdan at the 2022 ICM about a variety naturally attached to any stable vector bundle of rank 2 and degree $2g- 1$ on a smooth projective complex curve of genus $g$.
Externí odkaz:
http://arxiv.org/abs/2411.02069
Autor:
Vakil, Ravi, Vemulapalli, Sameera
A degree $d$ genus $g$ cover of the complex projective line by a smooth curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. Which bundles are possible? Equivalently, which $\mathbb{P}^{d-2}$-bundles over $\m
Externí odkaz:
http://arxiv.org/abs/2410.22531
Autor:
Castorena, Abel, Hitching, George H.
There is a well studied notion of GIT-stability for coherent systems over curves, which depends on a real parameter $\alpha$. For generated coherent systems, there is a further notion of stability derived from Mumford's definition of linear stability
Externí odkaz:
http://arxiv.org/abs/2409.12794