Nodal curves and polarizations with good properties

Brivio, Sonia; Favale, Filippo F.

doi:10.1007/s13163-021-00404-z

Cited by 3 publications

(1 citation statement)

References 23 publications

(31 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where p g pC i q denotes the genus of the curve C i . As explained in [BF22,§1], this condition is equivalent to δ ´ℓ ě 1, where δ is the number of nodal singularities of C.…”

Section: Introductionmentioning

confidence: 99%

Geometric G-functions and Atypicality

Urbanik¹

2023

Preprint

View full text Add to dashboard Cite

In a seminal research manuscript, André showed how the theory of G-functions could be used to give height bounds on the moduli of smooth projective algebraic varieties acquiring non-generic algebraic cycles. The method was limited by the lack of a suitable cohomological interpretation for these G-functions at finite places. In this paper we use recent developments in p-adic Hodge theory to remove this constraint.With respect to André's strategy for producing height bounds from algebraic relations on G-function values at special points, we give a general method for producing relations that hold at all finite places, and show that producing relations at the infinite places is the essential difficulty. This leads to new cases of the Zilber-Pink conjecture, as well as new height bounds on special moduli, including the first unconditional finiteness results for CM moduli in non-Shimura settings.As a more technical contribution, we introduce a refinement of the Pila-Zannier strategy capable of handling Zilber-Pink-type atypical intersection problems in arbitrary dimension and for arbitrary smooth projective families.

show abstract

“…where p g pC i q denotes the genus of the curve C i . As explained in [BF22,§1], this condition is equivalent to δ ´ℓ ě 1, where δ is the number of nodal singularities of C.…”

Section: Introductionmentioning

confidence: 99%

Geometric G-functions and Atypicality

Urbanik¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

Higher-rank Brill-Noether loci on nodal reducible curves

Brivio

Favale²

2023

Geom Dedicata

View full text Add to dashboard Cite

In this paper, we deal with Brill-Noether theory for higher-rank sheaves on a polarized nodal reducible curve $$(C,{{\,\mathrm{\underline{w}}\,}})$$ ( C , w ̲ ) following the ideas of Brambila-Paz et al. (J Algebraic Geom 6(4): 645–669, 1997). We study the Brill-Noether loci of $${{\,\mathrm{\underline{w}}\,}}$$ w ̲ -stable depth one sheaves on C having rank r on all irreducible components and having small slope. In analogy with what happens in the smooth case, we prove that these loci are closely related to BGN extensions. Moreover, we produce irreducible components of the expected dimension for these Brill-Noether loci.

show abstract

Coherent systems and BGN extensions on nodal reducible curves

Brivio

Favale

2022

Int. J. Math.

View full text Add to dashboard Cite

Let [Formula: see text] be a polarized nodal reducible curve. In this paper, we consider coherent systems of type [Formula: see text] on [Formula: see text] with [Formula: see text]. We prove that the moduli spaces of [Formula: see text]-stable coherent systems stabilize for large [Formula: see text] and we generalize several results known for the irreducible case when we choose a good polarization. Then, we study in detail the components of moduli spaces containing coherent systems arising from locally free sheaves.

show abstract

Nodal curves and polarizations with good properties

Cited by 3 publications

References 23 publications

Geometric G-functions and Atypicality

Geometric G-functions and Atypicality

Higher-rank Brill-Noether loci on nodal reducible curves

Coherent systems and BGN extensions on nodal reducible curves

Contact Info

Product

Resources

About