Numerical adjunction formulas for weighted projective planes and lattice point counting

Cogolludo-Agustín, José Ignacio; Martín-Morales, Jorge; Ortigas-Galindo, Jorge

doi:10.1215/21562261-3600184

Cited by 6 publications

(10 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The moreover part is equivalent to proving N L (g) = N L (f ) for any generic germ g ∈ O X (k). This is a consequence of Proposition 1.6 since [9,18]), one can calculate this invariant using the generic germ provided in Theorem 0.1. On the other hand, the recursive formula for δ X (f ) is given in [8].…”

Section: Problem 24 (Coin Change-making Problem)mentioning

confidence: 91%

“…where ω = d − a − b is the degree of the canonical divisor on X. Let us now fix a Q-resolution π : Y → X of D. The notion of log-resolution logarithmic eigenmodule (LR for short) is defined in [19,9] as…”

Section: Settings and Definitionsmentioning

confidence: 99%

“…However, note that L p it must be a convenient L p -Newton polygon. The invariant µ Lp is defined as (9) µ…”

Section: N By Calculating the Intersection Multiplicity Of A Germ F ∈...mentioning

confidence: 99%

“…Calculation of Newton numbers. To end this section we will give some formulas to calculate the Newton numbers µ X (k) := µ L(k) of a quotient surface singularity X = X(d; 1, q) as defined in (9). In order to do so we need to introduce some notation.…”

Section: 5mentioning

confidence: 99%

“…In a related context, let X = P 2 (w 0 , w 1 , w 2 ) be a weighted projective plane and D = {f = 0} a quasi-projective curve of degree k in X. In [9] the following Numerical Adjunction Formula was proven (1)…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The space of curvettes of quotient singularities and associated invariants

Cogolludo-Agustín¹,

Martín-Morales²

2015

Preprint

View full text Add to dashboard Cite

This paper deals with a complete invariant ∆ X for cyclic quotient surface singularities. This invariant appears in the Riemann Roch and Numerical Adjunction Formulas for normal surface singularities. Our goal is to give an explicit formula for ∆ X based on the numerical information of X, that is, d and q as in X = X(d; 1, q). In the process, the space of curvettes and generic curves is explicitly described. We also define and describe other invariants of curves in X such as the LR-logarithmic eigenmodules, δ-invariants, and their Milnor and Newton numbers.

show abstract

Section: Problem 24 (Coin Change-making Problem)mentioning

confidence: 91%

Section: Settings and Definitionsmentioning

confidence: 99%

“…However, note that L p it must be a convenient L p -Newton polygon. The invariant µ Lp is defined as (9) µ…”

Section: N By Calculating the Intersection Multiplicity Of A Germ F ∈...mentioning

confidence: 99%

Section: 5mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The space of curvettes of quotient singularities and associated invariants

Cogolludo-Agustín¹,

Martín-Morales²

2015

Preprint

View full text Add to dashboard Cite

show abstract

The correction term for the Riemann–Roch formula of cyclic quotient singularities and associated invariants

Cogolludo-Agustín

Martín-Morales

2018

Rev Mat Complut

Self Cite

View full text Add to dashboard Cite

This paper deals with the invariant R X called the RR-correction term, which appears in the Riemann Roch and Numerical Adjunction Formulas for normal surface singularities. Typically, R X = δ top X − δ an X decomposes as difference of topological and analytical local invariants of its singularities. The invariant δ top X is well understood and depends only on the dual graph of a good resolution. The purpose of this paper is to give a new interpretation for δ an X , which in the case of cyclic quotient singularities can be explicitly computed via generic divisors.We also include two types of applications: one is related to the McKay decomposition of reflexive modules in terms of special reflexive modules in the context of the McKay correspondence. The other application answers two questions posed by Blache [5] on the asymptotic behavior of the invariant R X of the pluricanonical divisor.

show abstract

Delta invariant of curves on rational surfaces I. An analytic approach

Cogolludo-Agustín

Tamás

Martín-Morales

et al. 2021

Commun. Contemp. Math.

Self Cite

View full text Add to dashboard Cite

We prove that if [Formula: see text] is a reduced curve germ on a rational surface singularity [Formula: see text] then its delta invariant can be recovered by a concrete expression associated with the embedded topological type of the pair [Formula: see text]. Furthermore, we also identify it with another (a priori) embedded analytic invariant, which is motivated by the theory of adjoint ideals. Finally, we connect our formulae with the local correction term at singular points of the global Riemann–Roch formula, valid for projective normal surfaces, introduced by Blache.

show abstract

Numerical adjunction formulas for weighted projective planes and lattice point counting

Cited by 6 publications

References 23 publications

The space of curvettes of quotient singularities and associated invariants

The space of curvettes of quotient singularities and associated invariants

The correction term for the Riemann–Roch formula of cyclic quotient singularities and associated invariants

Delta invariant of curves on rational surfaces I. An analytic approach

Contact Info

Product

Resources

About