Picture taken at Poland, poster presentation of Abelian carpets
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Research
Research
My research in Algebraic Geometry focuses on the following three areas:
I.) Syzygies of Projective varieties
II.) Deformation Theory and Moduli
III.) Vanishing Theorems in Hodge theory
Syzygies of projective varieties
Syzygies of projective varieties
In syzygies my work is concerned with the end of the resolution of projective varieties. In my work I found that embeddings of projective varieties by complete linear series with sufficient positivity do not have weight one syzygies from the end of the resolution till a certain stage. I found optimal conditions on the positivity of the line bundles for which this vanishing is true.
Publications and Projects
Publications and Projects
1.) Vanishing of weight one syzygies of projective varieties
Preprint link: arxiv.2511.12994
2.) Vanishing of weight one syzygies for adjoint linear series of projective varieties (in progress)
Deformation Theory and Moduli Spaces
Deformation Theory and Moduli Spaces
In recent years, the study of ribbons and ropes has taken on a completely different direction through the work of P. Bangere, F. J. Gallego and M. Gonza ́lez where multiple structures and their smoothings are investigated via deformations of morphisms. These techniques have been applied in a variety of contexts: constructing smooth subcanonical subvarieties of projective space with prescribed invariants and codimension, describing components of moduli spaces of varieties of general type, establishing the existence of normal crossings of Fano varieties in projective space and their smoothings among others.
My work is taking the first steps towards showing this results on Abelian varieties by smoothing similar multiple structures called Abelian carpets have smoothings by families of polarized Abelian surfaces and that these carpets are in the smooth component of the Hilbert scheme of polarized Abelian surfaces.
Publications and Projects
Publications and Projects
1.) Smooting of Abelian carpets on elliptic ruled surfaces (in progress)
Vanishing Theorems in Hodge theory
Vanishing Theorems in Hodge theory
I In an ongoing project I am investigating the following:
a.) Lower bounds on m such that the adjoint linear series |KX+mB| on a smooth projective variety X, with B ample and base-point-free and KX canonical divisor, satisfy the Torelli theorem for hypersurfaces
and
b.) Optimal lower bounds (linear on dimension) towards Madhav Nori's conjecture on cycle-theoretic connectivity which in the lines of the Nori connectivity theorem.
Publications and Projects
Publications and Projects
1.) Effective bounds vanishing theorems and applications to Torelli and Nori connectivity theorems (in progress)
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