Now showing items 1-9 of 9

    • Criterion for logarithmic connections with prescribed residues 

      Biswas, I.; Dan, A.; Paul, A. (2017-04-01)
      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. (2019-04-16)
      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 well-known 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. (2019-12-01)
      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. (2017-01-10)
      Classically, there exists a determinant map from the moduli space of semi-stable 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 Noether-Lefschetz 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. (2017-01-10)
      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. (2017-01-10)
      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.