# AGANT SEMINAR

### (Algebraic Geometry, Algebra and Number Theory Seminar)

a joint venture of UNT, UTA and TCU

*``Zero Loci of Holomorphic Forms and Birational
Geometry''
*

**Abstract:**
The zero locus of a holomorphic vector field has been a subject
of study for a long time on a compact complex manifold. For example, the
residue theorem of Bott relates the zero locus of a vector field with the
Chern numbers of the manifold (which, in high-brow terms, explains why a
vector field on a sphere has to vanish at some point). Surprisingly, not
much has been done about the zero locus of a holomorphic form. Through
studying various problems in birational geometry of algebraic varieties of
general type (in dimension 1, theses are Riemann surfaces with more than
one hole), we conjecture that a holomorphic form has to vanish somewhere on
a variety of general type. In this talk, work done, and work in progress,
towards verifying this conjecture will be presented.

Please mention/email this talk to any interested parties not on this email
list, and to your students if you are teaching an advanced undergraduate
algebra class or a graduate algebra class.

If you are travelling from out of town, then a map of UTA may be found at
http://www.uta.edu/maps/. Note that
PKH is the triangular building in the south-central region of the map next
to the ``garage'' & is on Nedderman Drive between College St & West St.
Parking is available in the nearby (just south of PKH) parking lots with a
UTA permit. Visitor (free), & metered, parking is available by Davis Hall
(marked DH in South West part of map). A parking garage (expensive) is
nextdoor to Pickard Hall (use West St to get to it). Note that if heading
south on Cooper, then no left turn is allowed to Nedderman Drive.
Recommended route from UNT: eventually head south on Hwy 360 (or Industrial
Blvd = Collins) West on Abram, south on Pecan, West on Nedderman. Then use
map. From TCU: east on I30, exit Cooper, South on Cooper (but there is
currently construction on Cooper and so the possibility of heavy delays, so
you might prefer to use Fielder, heading South to W Mitchell, East on
W Mitchell to Cooper), then use map. From anywhere else: good luck!
Note that PKH 487 is on the 4th floor of PKH; turn right out of elevator on
4th floor.

Questions, etc on arrangements/directions? Contact
Michaela Vancliff.
Please RSVP if coming from out of town, since, if you are a little late, we
will delay the start of the talk for you.

THE NEXT SEMINAR WILL BE FRI MAR 28 AT 4 PM BY ZE-LI DOU AT TCU.