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Nagaraj, D. S.
- Fourier-Mukai Transform of Vector Bundles on Surfaces to Hilbert Scheme
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1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, IN
2 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, IN
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, IN
2 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 32, No 1 (2017), Pagination: 43-50Abstract
Let S be an irreducible smooth projective surface defined over an algebraically closed field k. For a positive integer d, let Hilbd (S) be the Hilbert scheme parametrizing the zero-dimensional subschemes of S of length d. For a vector bundle E on S, let H(E) → Hilbd (S) be its Fourier–Mukai transform constructed using the structure sheaf of the universal subscheme of S × Hilbd (S) as the kernel. We prove that two vector bundles E and F on S are isomorphic if the vector bundles H(E) and H(F) are isomorphic.
- Morphisms from ℙ2 to Gr(2,ℂ4)
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1 Laboratoire De Mathematiques De Lens EA 2462, Faculte Des Sciences Jean Perrin Rue Jean Souvraz, SP18 F-62307, Lens Cedex, FR
2 Mathematiques-Bat. M2, Universite Lille 1, F-59655 Villeneuve D’Ascq Cedex, FR
3 Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600113, IN
1 Laboratoire De Mathematiques De Lens EA 2462, Faculte Des Sciences Jean Perrin Rue Jean Souvraz, SP18 F-62307, Lens Cedex, FR
2 Mathematiques-Bat. M2, Universite Lille 1, F-59655 Villeneuve D’Ascq Cedex, FR
3 Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600113, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 26, No 3 (2011), Pagination: 321-332Abstract
In this note we study morphisms from ℙ2 to Gr(2,ℂ4) from the point of view of the cohomology class they represent in the Grassmannian. This leads to some new result about projection of d-uple embedding of ℙ2 to ℙ5.- Secant Bundles on Second Symmetric Power of a Curve
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Authors
Affiliations
1 Laboratoire De Mathematiques De Lens EA 2462 Faculte Des Sciences Jean Perrin Rue Jean Souvraz, SP18 F-62307 LENS Cedex, FR
2 Mathematiques-Bat. M2, Universite Lille 1, F-59655 Villeneuve D’Ascq Cedex, FR
3 Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600113, IN
1 Laboratoire De Mathematiques De Lens EA 2462 Faculte Des Sciences Jean Perrin Rue Jean Souvraz, SP18 F-62307 LENS Cedex, FR
2 Mathematiques-Bat. M2, Universite Lille 1, F-59655 Villeneuve D’Ascq Cedex, FR
3 Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600113, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 26, No 2 (2011), Pagination: 181-194Abstract
For a line bundle L on non-singular irreducible curve C one has a rank two vector bundle EL on the second symmetric power S2(C) of C. The aim of this note is to investigate some natural properties of the vector bundle EL.- Cycle Class Map and Restriction of Subvarieties
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Authors
Affiliations
1 Stat-Math Unit, Indian Statistical Institute, Bangalore Centre, 8th Mile, Mysore Road, Bangalore-560 059, IN
2 Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai 600 113, IN
1 Stat-Math Unit, Indian Statistical Institute, Bangalore Centre, 8th Mile, Mysore Road, Bangalore-560 059, IN
2 Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai 600 113, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 17, No 2 (2002), Pagination: 85-91Abstract
The famous Lefschetz’s hyperplane theorem states the following: Let Y be a smooth hyperplane section of a smooth projective variety X and let i : Y → X be the inclusion map.