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Dr. Seshadri Chintapalli

Assistant Professor

Mathematical Sciences

seshu@iiserbpr.ac.in

6546464654

   

Academic Background

  • MSc (Mathematics), Andhra University, Vizag

  • Ph.D. (Mathematics), The Institute of Mathematical Sciences (IMSc), Chennai.

Professional Experience 

  • Postdoctoral Experience:
    TIFR, Mumbai, Feb 2014–Jul 2015.
    CMI, Chennai, Aug 2015–Aug 2017.
    HRI, Allahabad, Sep 2017–March 2018.

  • Inspire Faculty, (Apr 2018–Jul 2018), Harish-Chandra Research Institute, Allahabad

  • Assistant Professor (Aug 2018–Jun 2019), University of Hyderabad

Awards and Memberships

  • Qualified Graduate Aptitude Test in Engineering (GATE), in 2008.

  • Qualified CSIR from the Council of Scientific and Industrial Research, India, 2008.

  • Doctoral Fellowship awarded by IMSc, Chennai in 2011.

  • Post-Doctoral Fellowship awarded by TIFR, Mumbai, Feb–201.

  • Post-Doctoral Fellowship awarded by CMI, Chennai, Aug–2015.

  • Post-Doctoral Fellowship awarded by HRI, Allahabad, Sep–2017

  • DST-INSPIRE Faculty fellowship, Feb–2018.

Research Interests

  • Algebraic Geometry

  • Algebraic Geometry

  • Differential Geometry

Research Projects

  • Embedding properties of linear series on some smooth projective varieties.

In recent years, the problems related to linear series, specifically projective normality, normal presentation, and higher syzygies of an ample line bundle L on a smooth projective variety X have attracted considerable attention. The initial questions about projective normality and normal presentation on curves were proved by Castelnuova, Mattuck, Fujita and St-Donat. Later Mark Green unified the above concepts and introduced the Np-property, also called the p-th syzygy property for p ≥ 0, and generalized these results to a statement about syzygies. More precisely, if L is a line bundle on a curve C of genus g such that degree of L is at least 2g + 1 + p then L satisfies Np-property, for p ≥ 0.

In the case of higher dimensional varieties Mukai conjectured that for any smooth polarized projective variety (X, L), KX ⊗L ⊗p+4 satisfies Np-property, where KX denotes the canonical line bundle on X. Mukai’s conjecture has not yet been proved even for p = 0, but some significant work has been done in some special cases by Kempf, Y. Homma, Ein and Lazarsfeld. A stronger version of the Mukai conjecture in the case of Enriques surfaces and for the property N0-property is proved by Gallego and Purnaprajna. Gallego and Purnaprajna have done some nice work regarding syzygy properties on surfaces and three folds. In the case of abelian varieties Lazarsfeld conjectured that if L is an ample line bundle on abelian variety X then L ⊗p+3 satisfies Np-property.

On the other hand, Fujita’s conjecture on the very ampleness of a line bundle has attracted attention in the past years. Indeed, if L is an ample line bundle on an algebraic variety X of dimension n, then KX ⊗ L ⊗n+2 is very ample. Fujita’s conjecture has been proven for algebraic surfaces but this problem is still open for higher dimensional varieties.

NOTE: The questions related to very ampleness, k-jet ampleness, and syzygies are completely known in the case of abelian varieties.


We investigate the above properties of linear series on some smooth projective varieties.

Key Publications

  1. Semistability of logarithmic cotangent bundle on some projective manifolds. S. Chintapalli and Jaya N Iyer, Communications in Algebra, 42, 1732–1746, 2014.
  2. Embedding theorems on hyperelliptic varieties, S. Chintapalli and Jaya N Iyer Geom. Dedicata, 171, 249–264 (2014).
  3. On Syzygies of Projective bundles over Abelian varieties, S. Chintapalli Journal of Pure and Applied Algebra, Volume 223, Issue 6, June 2019, Pages 2413-2424

Contact Details

Full Name

Seshadri Chintapalli


Email

seshu@iiserbpr.ac.in


Contact

6546464654


Address

IISER Berhampur