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Item type:Publication, Algebraic quotients and Geometric Invariant Theory(Universidad Nacional de Trujillo, 2020-06-30)The quotient of an algebraic variety by action of an algebraic group does not always has a variety structure. The aim of this work is to describe a methodfor constructing good quotients, in the sense of Geometric invariant theory, in algebraicgeometry. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Geometry of Horospherical Varieties of Picard Rank One(Oxford University Press, 2020-10-29)Abstract We study the geometry of smooth non-homogeneous horospherical varieties of Picard rank one. These have been classified by Pasquier and include the well-known odd symplectic Grassmannians. We focus our study on quantum cohomology, with a view towards Dubrovin’s conjecture. We start with describing the cohomology groups of smooth horospherical varieties of Picard rank one. We show a Chevalley formula for these and establish that many Gromov–Witten invariants are enumerative. This enables us to prove that in many cases the quantum cohomology is semisimple. We give a presentation of the quantum cohomology ring for odd symplectic Grassmannians. In the last sections, we turn to derived categories of coherent sheaves. We first discuss a general construction of exceptional bundles on horospherical varieties. We work out in detail the case of the horospherical variety associated to the exceptional group $G_2$ and construct a full rectangular Lefschetz exceptional collection in the derived category. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory(Mathematical Sciences Publishers, 2021-01-01)We produce a Grothendieck transformation from bivariant operational K-theory to Chow, with a Riemann-Roch formula that generalizes classical Grothendieck-Verdier-Riemann-Roch. We also produce Grothendieck transformations and Riemann-Roch formulas that generalize the classical Adams-Riemann-Roch and equivariant localization theorems. As applications, we exhibit a projective toric variety X whose equivariant K-theory of vector bundles does not surject onto its ordinary K-theory, and describe the operational K-theory of spherical varieties in terms of fixed-point data. In an appendix, Vezzosi studies operational K-theory of derived schemes and constructs a Grothendieck transformation from bivariant algebraic K-theory of relatively perfect complexes to bivariant operational K-theory. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Bivariant K-theory of locally convex Z-graded algebras(Universidad Nacional de Trujillo, 2022-06-30)In the present work, we describe some results about the K-theory of Z-graded algebras. First, in the context of C* algebras, we begin with the Pimsner-Voiculescu sequence for crossed products and its generalizations. We will see that there are results analog to these in the context of locally convex algebras and we conclude with results for generalized Weyl algebras. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Complete transversal and formal normal forms of germs of vector fields(Sociedade Brasileira de Matemática, 2022-12-26)In this work, inspired by the technique of the complete transversal, used for the classification of plane branches, developed by Hefez, A. and Hernandes, M., as well as Bruce, J.W., Kirk, N.P. and du Plesis, A.A., study the singularities of applications, we establish a classification of vector fields through their normal forms. In the case of vector fields with non zero linear part in $(\mathbb{C}^{2}, 0) $ and nilpotent fields in $(\mathbb {C}^{n}, 0), n\geq 2$ we recover the classical normal forms for those fields, and we provide a formal normal form different from Takens in dimension 2. Likewise, we obtain the normal form for the vector fields in $(\mathbb{C},0)$ of any multiplicity. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, On the existence of holomorphic foliations on Hopf manifolds(Universidad Nacional Mayor de San Marcos, 2024-12-30)En este artículo, investigamos el problema de la existencia de foliaciones holomorfas en variedades de Hopf de dimensión 3, con un enfoque particular en las variedades de tipo excepcional. Las variedades de Hopf, al ser variedades complejas compactas y no kählerianas, ofrecen un entorno fértil para el análisis de fenómenos no triviales en el estudio de foliaciones holomorfas. En particular, estas variedades presentan estructuras geométricas que permiten la aparición de comportamientos dinámicos complejos, lo que las convierte en un caso de especial interés. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Transversely Product Singularities of Foliations in Projective Spaces(Academie des sciences, 2023-01-01)We prove that a transversely product component of the singular set of a holomorphic foliation on ℙ n is necessarily a Kupka component. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Beglund-Hübsch Transpose and Sasaki-Einstein Rational Homology 7-Spheres(Cornell University, 2023-11-27)We show that links of invertible polynomials coming from the Johnson and Kollár list of Kähler-Einstein 3-folds that are rational homology 7-spheres remain rational homology 7-spheres under the so-called Berglund-Hübsch transpose rule coming from classical mirror symmetry constructions. Actually, this rule produces twins, that is, links with same degree, Milnor number and homology H_3, with the exception of iterated Thom-Sebastiani sums of singularities of chain and cycle type, where the torsion and the Milnor number may vary. The Berglund-Hübsch transpose rule not only gives a framework to better understand the existence of SasakiEinstein twins but also gives a mechanism for producing new examples of Sasaki-Einstein twins in the rational homology 7 -sphere setting. We also give reasonable conditions for a Sasaki-Einstein rational homology 7-sphere to remain Sasaki-Einstein under the BH-transpose rule. In particular, we found 75 new examples of Sasaki-Einstein rational homology 7-spheres arising as links of not well-formed hypersurface singularities. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, On the Zariski invariant of plane branches(Polish Academy of Sciences::will be referenced::ROR-ID, 2026-03-16)We show how to obtain the Zariski invariant of a plane branch employing the contact order or the intersection multiplicity with elements in a particular family of curves, and we present some consequences of this result.2 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, On a Mattei–Salem theorem(Polish Academy of Sciences, 2025-02-26)We investigate the relationship between the valuations of a germ of a singular foliation $\mathcal F$ on the complex plane and those of a balanced equation of separatrices for $\mathcal F$, extending a theorem by Mattei–Salem. Under certain conditions, we also derive inequalities involving the valuation, tangency excess, and degree of a holomorphic foliation $\mathcal F$ on the complex projective plane.11