Browsing Singularity Theory and Algebraic Geometry by Author "Dan, A."
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Criterion for logarithmic connections with prescribed residues
Biswas, I.; Dan, A.; Paul, A. (20170401)A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset ... 
Examples of varieties with index one on C1 fields
Dan, A.; Kaur, I. (20190416)Let K be the fraction field of a Henselian discrete valuation ring with algebraically closed residue field k. In this article we give a sufficient criterion for a projective variety over such a field to have index 1. 
Local Topological Obstruction For Divisors
Biswas, I.; Dan, A. (2020)Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is wellknown that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in ... 
Logarithmic connections on principal bundles over a Riemann surface
Biswas, I.; Dan, A.; Paul, A.; Saha, A. (2017)Let $E_G$ be a holomorphic principal $G$bundle on a compact connected Riemann surface $X$, where $G$ is a connected reductive complex affine algebraic group. Fix a finite subset $D\, \subset\, X$, and for each $x\,\in\, ... 
Neron models of intermediate Jacobians associated to moduli spaces
Dan, A.; Kaur, I. (20191201)Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projective curves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$ with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$ ... 
A note on the determinant map
Dan, A.; Kaur, I. (20170110)Classically, there exists a determinant map from the moduli space of semistable sheaves on a smooth, projective variety to the Picard scheme. Unfortunately, if the underlying variety is singular, then such a map does not ... 
On a conjecture of harris
Dan, A. (2019)For d ≥ 4, the NoetherLefschetz locus NLd parametrizes smooth, degree d sur faces in P3 with Picard number at least 2. A conjecture of Harris states that there are only finitely many irreducible components of the ... 
Singularities of the Hilbert scheme of effective divisors
Dan, A. (20170110)In this article, we study the Hilbert scheme of effective divisors in smooth hypersurfaces in $\mathbb{P}^3$, a topic not extensively studied. We prove that there exists such effective divisors $D$ satisfying the property: ... 
A specialization property of index
Dan, A.; Kaur, I. (20170110)In [Kol13] Kollár defined $i$th index of a proper scheme over a field. In this note we study how index behaves under specialization, in any characteristic.