Algebraic Geometry authors/titles "new.AG"

# Algebraic Geometry

## New submissions

[ total of 15 entries: 1-15 ]
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### New submissions for Wed, 5 Jan 22

[1]
Title: Koszul modules with vanishing resonance in algebraic geometry
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)

We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace in the second wedge product of a vector space. Previously Koszul modules of finite length have been used to give a proof of Green's Conjecture on syzygies of generic canonical curves. We now give applications to effective stabilization of cohomology of thickenings of algebraic varieties, divisors on moduli spaces of curves, enumerative geometry of curves on K3 surfaces and to skew-symmetric degeneracy loci. We also show that the stability of sufficiently positive rank 2 vector bundles on curves is governed by resonance.

[2]
Title: On the freeness of certain determinantal hypersurface arrangements in $\mathbb{P}^{14}$
Subjects: Algebraic Geometry (math.AG)

In the present note we study determinantal arrangements constructed with use of the $3$-minors of a $3 \times 5$ generic matrix of indeterminates. In particular, we show that certain naturally constructed hypersurface arrangements in $\mathbb{P}^{14}_{\mathbb{C}}$ are free.

[3]
Title: Applications of the fibration method for zero-cycles to the Brauer-Manin obstruction to the existence of zero-cycles on certain varieties
Authors: Evis Ieronymou
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)

We study the Brauer-Manin obstruction to the existence of zero-cycles of degree $d$ on certain classes of varieties over number fields. We generalise existing results in the literature and prove some results about fibrations over the projective line, where the geometric Brauer group of the generic fibre is not assumed to be finite. The idea is to assume that the Brauer-Manin obstruction to the Hasse principle is the only one for certain fibres and then deduce analogous results for zero-cycles.

[4]
Title: On the Log Abundance for Compact Kähler $3$-folds
Subjects: Algebraic Geometry (math.AG); Complex Variables (math.CV)

In this article we show that if $(X, \Delta)$ is a log canonical compact K\"ahler $3$-fold such that $K_X+\Delta$ is nef and the numerical dimension $\nu(K_X+\Delta)\neq 2$, then $K_X+\Delta$ is semi-ample.

[5]
Title: On the $p$-adic theory of local models
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)

We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models of local Shimura varieties and the test function conjecture of Haines--Kottwitz in this setting. In order to achieve this, we establish the specialization principle for well-behaved $p$-adic kimberlites, show that these include the v-sheaf local models, determine their special fibers using hyperbolic localization for the \'etale cohomology of small v-stacks and analyze the resulting specialization morphism using convolution.

### Cross-lists for Wed, 5 Jan 22

[6]  arXiv:2201.00837 (cross-list from hep-th) [pdf, ps, other]
Title: Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Algebraic Geometry (math.AG); Number Theory (math.NT)

We present a geometric derivation of all-multiplicity (single-trace) tree-level Einstein Yang-Mills (EYM) amplitudes involving r gravitons and n gluons by a bilinear of two twisted differential forms on the moduli space of Riemann spheres with r+n punctures. The differential forms are gained by studying the underlying superstring disk amplitude and proposing an embedding of the disk onto the sphere. This map can be interpreted as a geometrical map from the open superstring to a heterotic or ambitwistor string structure. Then, the twisted intersection number of the two (r+n)-forms, which is obtained by integrating over the moduli space of Riemann sphere with r+n punctures, reproduces in the infinite inverse string tension limit $\alpha'\!\rightarrow\! \infty$ the corresponding CHY formula of the EYM amplitude. To bolster our findings we study the disk amplitude of open and closed strings using the Grassmann description of the underlying superstring amplitude, map it to a closed string amplitude and consider the $\alpha'\!\rightarrow\! \infty$ limit.

[7]  arXiv:2201.01028 (cross-list from math.CO) [pdf, ps, other]
Title: The $4 \times 4$ minors of a $5 \times 5$ symmetric matrix are a tropical basis
Authors: Dylan Zwick
Comments: 34 pages, 2 figures. arXiv admin note: text overlap with arXiv:2112.14945
Subjects: Combinatorics (math.CO); Algebraic Geometry (math.AG)

This paper proves the $4 \times 4$ minors of a $5 \times 5$ symmetric matrix of indeterminates are a tropical basis.

### Replacements for Wed, 5 Jan 22

[8]  arXiv:2003.04714 (replaced) [pdf, ps, other]
Title: Les suites spectrales de Hodge-Tate
Comments: 407 pages, in French. Revised version according to the referees' reports. Among the improvements, we prove a local version of the relative Hodge-Tate spectral sequence over a small affine scheme (1.2.2) as a consequence of the global version (1.4.5) and a cohomological descent in the Faltings topos (4.6.30); an error has been fixed in 5.5.13 and 5.5.15. arXiv admin note: substantial text overlap with arXiv:1509.03617
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[9]  arXiv:2007.15595 (replaced) [pdf, other]
Title: On the body of ample angles of asymptotically log Fano varieties
Comments: v2: Theorem 1.4 has been improved and now completely settles Problem 1.3; v3: final version to appear in Rendiconti del Circolo Matematico di Palermo
Subjects: Algebraic Geometry (math.AG)
[10]  arXiv:2103.04268 (replaced) [pdf, ps, other]
Title: The $d$-ampleness on quasi-elliptic surfaces
Authors: Yongming Zhang
Subjects: Algebraic Geometry (math.AG)
[11]  arXiv:2107.08603 (replaced) [pdf, ps, other]
Title: The motivic nearby cycle in positive characteristic
Subjects: Algebraic Geometry (math.AG); K-Theory and Homology (math.KT)
[12]  arXiv:2111.09911 (replaced) [pdf, ps, other]
Title: Birational rigidity and K-stability of Fano hypersurfaces with ordinary double points
Comments: v3: 15 pages, fixes an error in the previous version of Lemma 2.17 kindly pointed out by Kento Fujita and Yuga Tsubouchi
Subjects: Algebraic Geometry (math.AG)
[13]  arXiv:2111.10740 (replaced) [pdf, ps, other]
Title: Zeta function of projective hypersurfaces with ADE singularities
Authors: Matthew Cheung
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[14]  arXiv:2112.12679 (replaced) [pdf, ps, other]
Title: Topologization and Functional Analytification II: $\infty$-Categorical Motivic Constructions for Homotopical Contexts
Authors: Xin Tong
Comments: 112 pages. This is based on the author's UCSD dissertation on the Geometric and Representation Theoretic Aspects of p-adic Motives. The fourth version
Subjects: Algebraic Geometry (math.AG); Number Theory (math.NT)
[15]  arXiv:2107.09880 (replaced) [pdf, ps, other]
Title: Quantum cohomology of symplectic flag manifolds
Authors: Jirui Guo, Hao Zou